1. bookVolume 37 (2021): Issue 4 (December 2021)
Journal Details
License
Format
Journal
eISSN
2001-7367
First Published
01 Oct 2013
Publication timeframe
4 times per year
Languages
English
access type Open Access

The Robin Hood Index Adjusted for Negatives and Equivalised Incomes

Published Online: 26 Dec 2021
Page range: 1047 - 1058
Received: 01 Oct 2019
Accepted: 01 Apr 2021
Journal Details
License
Format
Journal
eISSN
2001-7367
First Published
01 Oct 2013
Publication timeframe
4 times per year
Languages
English
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.

Keywords

Balestra, C., and R. Tonki. 2018. Inequalities in household wealth across OECD countries: Evidence from the OECD Wealth Distribution Database. OECD Statistics Working Paper Series. Available at: www.oecd.org. (accessed September 2019). Search in Google Scholar

CBS StatLine. 2020a. Inequlity of income and wealth (in Dutch). Available at: http://opendata.cbs.nl/statline/#/CBS/nl/dataset/84476NED/table?dl=49EF5 (accessed January 2021). Search in Google Scholar

CBS StatLine. 2020b. Welfare of households; key figures. Available at: http://opendata.cbs.nl/statline/#/CBS/en/dataset/83739ENG/table?dl=49EF4 (accessed January 2021). Search in Google Scholar

Chen, C.-N., T.-W. Tsaur, and T.-S. Rhai. 1982. “The Gini coefficient and negative income.” Oxford Economic Papers 34 (3): 473–478. http://dx.doi.org/10.1093/oxfordjournals.oep.a041563.10.1093/oxfordjournals.oep.a041563 Search in Google Scholar

Habib, E.A. 2012. “On the decomposition of the Schutz coefficient; an exact approach with an application.” Electronic Journal of Applied Statistical Analysis 5(2) : 187–198. DOI: http://dx.doi.org/10.1285/i20705948v5n2p187. Search in Google Scholar

OECD. 2013. OECD Framework for statistics on the distribution of household income, consumption and wealth. Available at: www.oecd.org (accessed September 2019). Search in Google Scholar

OECD. 2014. Focus on Inequality and Growth. Paris: OECD Publishing. Search in Google Scholar

OECD. 2015. In It Together: Why Less Inequality Benefits All. Paris: OECD Publishing. Search in Google Scholar

Pietra, G. 1915. “Delle relazioni tra indici di variabilità.” Atti del reale Istituto Veneto di Scienze, Lettere ed Arti 74(2). Search in Google Scholar

Pietra, G. 2014. “On the relations between variability indices (Note I).” METRON 72: 5–16. DOI: https://doi.org/10.1007/s40300-014-0034-3.10.1007/s40300-014-0034-3 Search in Google Scholar

Piketty, T. 2014. Capital in the Twenty-First Century. Harvard University Press.10.4159/9780674369542 Search in Google Scholar

Raffinetti, E., E. Siletti, and A. Vernizzi. 2015. “On the Gini coefficient normalization when attributes with negative values are considered.” Stat Methods Appl 24: 507–512. DOI: http://dx.doi.org/10.1007/s10260-014-0293-4.10.1007/s10260-014-0293-4 Search in Google Scholar

Ricci, U. 1916. “L’indice di variabilità e la curva dei redditi.” Giornale degli Economisti e Rivista di Statistica LIII: 177–228. serie terza, anno XXVII. Available at: https://www.jstor.org/stable/23225478 (accessed October 2021). Search in Google Scholar

Schutz, R. 1951. “On the measurement of income inequality.” The American Economic Review 41: 107–122. Available at: On the Measurement of Income Inequality (jstor.org) (accessed April 2021). Search in Google Scholar

United Nations. 2011. Canberra Group, Handbook on Household Income Statistics (second edition). New York and Geneva. Available at: Canbera_Handbook_2011_-WEB.pdf (unece.org) (accessed April 2021). Search in Google Scholar

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