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The Robin Hood Index Adjusted for Negatives and Equivalised Incomes

Author

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  • van den Brakel Marion

    (Statistics Netherlands, Department of Statistics on Labour, Income and Living conditions CBS-weg 11 6412EX Heerlen, the Netherlands.)

  • Lok Reinder

    (Statistics Netherlands, Department of Statistics on Labour, Income and Living conditions CBS-weg 11 6412EX Heerlen, the Netherlands.)

Abstract

Indisputable figures on income and wealth inequality are indispensable for politics, society and science. Although the Gini coefficient is the most common measure of inequality, the straightforward concept of the Robin Hood index (namely, the income share that has to be transferred from the rich to the poor to make everyone equally well off) makes it a more attractive measure for the general public. In a distribution with many negative values – particularly wealth distributions – the Robin Hood index can take on values larger than 1, indicating an intuitively impossible income transfer of more than 100%. This article proposes a method to normalise the Robin Hood index. In contrast to the original index, the normalised Robin Hood index always takes on values between 0 and 1 and ends up as the original index in a distribution without negatives. As inequality measures are commonly applied to equivalised income, we also introduce a method for adequately transferring equivalised incomes from the rich to the poor within the framework of the (normalised) Robin Hood index. An empirical application shows the effect of normalisation for the Robin Hood index, and compares it to the normalisation of the Gini coefficient from previous research.

Suggested Citation

  • van den Brakel Marion & Lok Reinder, 2021. "The Robin Hood Index Adjusted for Negatives and Equivalised Incomes," Journal of Official Statistics, Sciendo, vol. 37(4), pages 1047-1058, December.
    • Handle: RePEc:vrs:offsta:v:37:y:2021:i:4:p:1047-1058:n:6
    DOI: 10.2478/jos-2021-0044
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    References listed on IDEAS

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    1. Emanuela Raffinetti & Elena Siletti & Achille Vernizzi, 2015. "On the Gini coefficient normalization when attributes with negative values are considered," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 507-521, September.
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