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Estimating Income Inequality Using Single-Parameter Lorenz Curves: A New Proposal

Author

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  • José María Sarabia

    (University of Cantabria)

  • Vanesa Jordá

    (University of Cantabria)

  • Mercedes Tejería

    (University of Cantabria)

Abstract

In a recent paper, Paul and Shankar (2020) introduced a single-parameter Lorenz curve that provides an improved fit compared to many existing uniparametric models. This paper explores new properties of their model, offering a refined representation in terms of convex linear combinations of Lorenz curves. We also derive closed-form expressions for several inequality measures and examine the Lorenz ordering. However, we identify a key limitation: The Gini index for this curve is lower bounded at 0.418, making the model unsuitable for income distributions with lower inequality. To address this issue, we propose an alternative model that extends the range of the Gini index, allowing for greater flexibility in representing income distributions across a wider range of inequality levels. Our results suggest that the Lorenz curve proposed in this paper surpasses the proposal by Paul and Shankar, even in countries with high inequality, where the constraint imposed by the Gini index is not binding.

Suggested Citation

  • José María Sarabia & Vanesa Jordá & Mercedes Tejería, 2025. "Estimating Income Inequality Using Single-Parameter Lorenz Curves: A New Proposal," Empirical Economics, Springer, vol. 69(2), pages 581-597, August.
    • Handle: RePEc:spr:empeco:v:69:y:2025:i:2:d:10.1007_s00181-025-02757-6
    DOI: 10.1007/s00181-025-02757-6
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    References listed on IDEAS

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    1. Ryu, Hang K. & Slottje, Daniel J., 1996. "Two flexible functional form approaches for approximating the Lorenz curve," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 251-274.
    2. Kakwani, N C & Podder, N, 1973. "On the Estimation of Lorenz Curves from Grouped Observations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 278-292, June.
    3. José‐María Sarabia & Enrique Castillo & Daniel J. Slottje, 2001. "An Exponential Family of Lorenz Curves," Southern Economic Journal, John Wiley & Sons, vol. 67(3), pages 748-756, January.
    4. José María Sarabia & Vanesa Jordá & Carmen Trueba, 2017. "The Lamé class of Lorenz curves," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(11), pages 5311-5326, June.
    5. Satya Paul & Sriram Shankar, 2020. "An alternative single parameter functional form for Lorenz curve," Empirical Economics, Springer, vol. 59(3), pages 1393-1402, September.
    6. José-María Sarabia & Enrique Castillo & Daniel J. Slottje, 2001. "An Exponential Family of Lorenz Curves," Southern Economic Journal, Southern Economic Association, vol. 67(3), pages 748-756, January.
    7. 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.
    8. Dhongde, Shatakshee & Minoiu, Camelia, 2013. "Global Poverty Estimates: A Sensitivity Analysis," World Development, Elsevier, vol. 44(C), pages 1-13.
    9. José-María Sarabia & Enrique Castillo & Daniel J. Slottje, 2001. "An Exponential Family of Lorenz Curves," Southern Economic Journal, John Wiley & Sons, vol. 67(3), pages 748-756, January.
    10. Gholamreza Hajargasht & William E. Griffiths, 2020. "Minimum distance estimation of parametric Lorenz curves based on grouped data," Econometric Reviews, Taylor & Francis Journals, vol. 39(4), pages 344-361, April.
    11. Villasenor, JoseA. & Arnold, Barry C., 1989. "Elliptical Lorenz curves," Journal of Econometrics, Elsevier, vol. 40(2), pages 327-338, February.
    12. Ripsy Bandourian & Robert Turley & James McDonald, 2002. "A Comparison of Parametric Models of Income Distribution across Countries and over Time," LIS Working papers 305, LIS Cross-National Data Center in Luxembourg.
    13. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    14. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
    15. Vanesa Jorda & José María Sarabia & Markus Jäntti, 2021. "Inequality measurement with grouped data: Parametric and non‐parametric methods," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 964-984, July.
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