<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

The Robin Hood Index Adjusted for Negatives and Equivalised Incomes

Statistics Netherlands, Department of Statistics on Labour, Income and Living conditions

Journal of Official Statistics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"The Robin Hood Index Adjusted for Negatives and Equivalised Incomes"}

Indisputable figures on income and wealth inequality are indispensable for politics, society and science. Although the Gini coefficient is the most common...

The Robin Hood Index Adjusted for Negatives and Equivalised Incomes

Published Online: Dec 26, 2021

Page range: 1047 - 1058

Received: Oct 01, 2019

Accepted: Apr 01, 2021

DOI: https://doi.org/10.2478/jos-2021-0044

Keywords
Negative wealth, Pietra or Schutz index, normalisation, income inequality, Gini coefficient

© 2020 Marion van den Brakel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Robin Hood Index Adjusted for Negatives and Equivalised Incomes

Published Online: Dec 26, 2021

Page range: 1047 - 1058

Received: Oct 01, 2019

Accepted: Apr 01, 2021

DOI: https://doi.org/10.2478/jos-2021-0044

KeywordsNegative wealth, Pietra or Schutz index, normalisation, income inequality, Gini coefficient

© 2020 Marion van den Brakel et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Negative wealth, Pietra or Schutz index, normalisation, income inequality, Gini coefficient