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On Calculation of the Extended Gini Coefficient

Author

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  • Duangkamon Chotikapanich
  • William Griffiths

Abstract

The conventional formula for estimating the extended Gini coefficient is a covariance formula provided by Lerman and Yitzhaki (1989). We suggest an alternative estimator, obtained by approximating the Lorenz curve by a series of linear segments. In a Monte Carlo experiment designed to assess the relative bias and efficiency of the two estimators, we find that, when using grouped data with 20 or fewer groups, our new estimator has less bias and lower mean squared error than the covariance estimator. When individual observations are used, or the number of groups is 30 or more, there is little or no difference in the performance of the two estimators.

Suggested Citation

  • Duangkamon Chotikapanich & William Griffiths, 2001. "On Calculation of the Extended Gini Coefficient," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 47(4), pages 541-547, December.
    • Handle: RePEc:bla:revinw:v:47:y:2001:i:4:p:541-547
    DOI: 10.1111/1475-4991.00033
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    References listed on IDEAS

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    1. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    2. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
    3. John Creedy, 1996. "Fiscal Policy and Social Welfare," Books, Edward Elgar Publishing, number 797.
    4. Lerman, Robert I. & Yitzhaki, Shlomo, 1989. "Improving the accuracy of estimates of Gini coefficients," Journal of Econometrics, Elsevier, vol. 42(1), pages 43-47, September.
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    Cited by:

    1. Stephen P. Jenkins & Philippe Van Kerm, 2016. "Assessing Individual Income Growth," Economica, London School of Economics and Political Science, vol. 83(332), pages 679-703, October.
    2. Heshmati, Almas, 2004. "A Review of Decomposition of Income Inequality," IZA Discussion Papers 1221, Institute of Labor Economics (IZA).
    3. Heshmati, Almas, 2004. "Inequalities and Their Measurement," IZA Discussion Papers 1219, Institute of Labor Economics (IZA).
    4. Essama-Nssah, B., 2002. "Assessing the distributional impact of public policy," Policy Research Working Paper Series 2883, The World Bank.
    5. Diasakos, Theodoros M & Neymotin, Florence, 2013. "Coordination in Public Good Provision: How Individual Volunteering is Impacted by the Volunteering of Others," SIRE Discussion Papers 2013-119, Scottish Institute for Research in Economics (SIRE).
    6. repec:ebl:ecbull:v:4:y:2006:i:5:p:1-9 is not listed on IDEAS
    7. Rolf Aaberge, 2007. "Gini’s nuclear family," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 305-322, December.
    8. Lie Ma & Qiu Xie & Shiying Shi & Xiaosu Ye & Aifeng Zhao, 2017. "Regional Maldistribution of China’s Hospitals Based on Their Structural System," Sustainability, MDPI, vol. 9(6), pages 1-18, June.
    9. Theodoros M. Diasakos & Florence Neymotin, 2011. "Community Matters: How the Volunteering of Others Affects One's Likelihood of Engaging in Volunteer Work," Carlo Alberto Notebooks 209, Collegio Carlo Alberto.
    10. Araceli Ortega Diaz, 2004. "Assesment of the relationship between Inequality and Economic Growth: A panel Data Approach," Econometric Society 2004 Latin American Meetings 261, Econometric Society.
    11. Edna Schechtman & Ricardas Zitikis, 2006. "Gini indices as areas and covariances: what is the difference between the two representations?," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 385-397.
    12. Walter Piesch, 2005. "A look at the structure of some extended Ginis," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 263-296.
    13. Chameni Nembua, Célestin, 2008. "Measuring and explaining economic inequality: An extension of the Gini coefficient," MPRA Paper 31242, University Library of Munich, Germany, revised 2010.
    14. Xiao Ma & Feiran Wang & Jiandong Chen & Yang Zhang, 2018. "The Income Gap Between Urban and Rural Residents in China: Since 1978," Computational Economics, Springer;Society for Computational Economics, vol. 52(4), pages 1153-1174, December.
    15. Célestin Chameni Nembua, 2006. "Linking Gini to Entropy : Measuring Inequality by an interpersonal class of indices," Economics Bulletin, AccessEcon, vol. 4(5), pages 1-9.
    16. Shlomo Yitzhaki & Edna Schechtman, 2005. "The properties of the extended Gini measures of variability and inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 401-433.
    17. Diasakos, Theodoros M & Neymotin, Florence, 2013. "Coordination in Public Good Provision: How Individual Volunteering is Impacted by the Volunteering of Others," SIRE Discussion Papers 2013-119, Scottish Institute for Research in Economics (SIRE).

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D30 - Microeconomics - - Distribution - - - General

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