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Inequality Indices

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Lectures on Inequality, Poverty and Welfare

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 685))

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Abstract

This chapter presents the notion of inequality indices as functions that map the space of income distributions into the real numbers. We address here two specific questions. First, we discuss a set of properties, or requirements, that make a function a suitable candidate for an inequality index. Those properties include Normalisation, Symmetry, Population Replication, Principle of Transfers, Continuity, Scale Independence and Additive Decomposability. Second, we illustrate the difference between the notions of dispersion and inequality, by analysing the properties and key features of the variance and its related measures (standard deviation, coefficient of variation). We show that even though the variance satisfies most of the properties we may require for an inequality index, it is not a suitable inequality measure.

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Notes

  1. 1.

    This is not the only way of thinking of the evaluation of income distributions, but it is the dominant approach. Other approaches may look for a relative evaluation, that is, evaluating the inequality of a distribution with respect to others, but not in isolation.

  2. 2.

    In a richer context, anonymity and symmetry are not exactly the same. Yet here both properties are equivalent.

  3. 3.

    One can also think of intermediate situations. See Pfingsten (1986), Bossert and Pfingsten (1990), Del Río and Ruiz-Castillo (2000), Cowell (2003).

  4. 4.

    Note that one cannot explain total inequality as a weighted sum to within groups’ inequality. To see this, simply think of the case of a society made of two different groups (e.g. men and women), such that all agents within a group have the same income but the income between agents of different groups differ. Total inequality will be positive whereas within groups’ inequality is zero.

  5. 5.

    Those weights typically depend either on the population shares or on the income shares, or on both.

  6. 6.

    The variance is an absolute inequality index because adding the same amount of income to each agent does not change its value.

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Authors and Affiliations

  1. Department of Economics, Universidad Pablo de Olavide, Seville, Spain

    Antonio Villar

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  1. Antonio Villar
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Villar, A. (2017). Inequality Indices. In: Lectures on Inequality, Poverty and Welfare. Lecture Notes in Economics and Mathematical Systems, vol 685. Springer, Cham. https://doi.org/10.1007/978-3-319-45562-4_2

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