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Estimation of Gini coefficients using Lorenz curves

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  • Johan Fellman

Abstract

Primary income data yields the most exact estimates of the Gini coefficient. Using Lorenz curves, the Gini coefficient is defined as the ratio of the area between the diagonal and the Lorenz curve and the area of the whole triangle under the diagonal. Various attempts have been made to obtain accurate estimates. The trapezium rule is simple, but yields a positive bias for the area under the Lorenz curve and, consequently, a negative bias for the Gini coefficient. Simpson´s rule is better fitted to the Lorenz curve, but this rule demands an even number of subintervals of the same length. Lagrange polynomials of second degree can be considered as a generalisation of Simpson´s rule because they do not demand equidistant points. If the subintervals are of the same length, the Lagrange polynomial method is identical with Simpson´s rule. In this study, we compare different methods. When we apply Simpson´s rule, we mainly consider Lorenz curves with deciles. In addition, we use the trapezium rule, Lagrange polynomials and generalizations of Golden´s method (2008). No method is uniformly optimal, but the trapezium rule is almost always inferior and Simpson´s rule is superior. Golden´s method is usually of medium quality.

Suggested Citation

  • Johan Fellman, 2012. "Estimation of Gini coefficients using Lorenz curves," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 1(2), pages 1-3.
  • Handle: RePEc:spt:stecon:v:1:y:2012:i:2:f:1_2_3
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    Cited by:

    1. Johan Fellman, 2021. "Empirical Analyses of Income: Finland (2009) and Australia (1967-1968)," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 10(1), pages 1-3.
    2. John Creedy & S. Subramanian, 2022. "Mortality Comparisons ‘At a Glance’: A Mortality Concentration Curve and Decomposition Analysis for India," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 873-894, November.
    3. Julia Varlamova & Ekaterina Kadochnikova, 2023. "Modeling the Spatial Effects of Digital Data Economy on Regional Economic Growth: SAR, SEM and SAC Models," Mathematics, MDPI, vol. 11(16), pages 1-31, August.
    4. Lingyue Li & Zhixin Qi & Shi Xian & Dong Yao, 2021. "Agricultural Land Use Change in Chongqing and the Policy Rationale behind It: A Multiscale Perspective," Land, MDPI, vol. 10(3), pages 1-18, March.
    5. Johan Fellman, 2021. "Aspects of Pareto distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 10(1), pages 1-4.
    6. Louis Mesnard, 2022. "About some difficulties with the functional forms of Lorenz curves," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(4), pages 939-950, December.
    7. Banks, William, 2021. "When did Chile fall asleep? An assessment of national and regional income inequality in Chile, 1973-1990," LSE Research Online Documents on Economics 113197, London School of Economics and Political Science, LSE Library.

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