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A regression method for estimating Gini index by decile

Author

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  • Xiaobo Shen

    (Xiamen University)

  • Pingsheng Dai

    (Jimei University)

Abstract

Based on the three-parametric Lorenz curve proposed by Kakwani (1980), this paper builds a multiple linear regression model to estimate the parameters by the weighted least square method named the regression method. Using the Lorenz curve, the Gini index and its variance are then calculated. Compared to the error minimization technique, the regression method has a better performance in estimating the Gini index using Kakwani (1980)’s Lorenz curve and a dataset of sixteen economies from the United Nation University-World Income Inequality Database (UNU-WIID). The results also suggest that the regression method has an advantage when estimating the Gini index and fitting the income shares by decile for the medium and higher inequality economies. We find that the three-parametric Lorenz curve has a better performance than the double-parametric Lorenz curve, and the double-parametric Lorenz curve is superior to the single-parametric Lorenz curve, judged by the RMSE of the actual Gini index and the estimated ones.

Suggested Citation

  • Xiaobo Shen & Pingsheng Dai, 2024. "A regression method for estimating Gini index by decile," Palgrave Communications, Palgrave Macmillan, vol. 11(1), pages 1-8, December.
    • Handle: RePEc:pal:palcom:v:11:y:2024:i:1:d:10.1057_s41599-024-03701-2
    DOI: 10.1057/s41599-024-03701-2
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    References listed on IDEAS

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    1. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
    2. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    3. Chotikapanich, Duangkamon & Griffiths, William E. & Rao, D. S. Prasada, 2007. "Estimating and Combining National Income Distributions Using Limited Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 97-109, January.
    4. Chotikapanich, Duangkamon & Valenzuela, Rebecca & Rao, D S Prasada, 1997. "Global and Regional Inequality in the Distribution of Income: Estimation with Limited and Incomplete Data," Empirical Economics, Springer, vol. 22(4), pages 533-546.
    5. 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.
    6. Chotikapanich, Duangkamon & Griffiths, William E, 2002. "Estimating Lorenz Curves Using a Dirichlet Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 290-295, April.
    7. Kakwani, Nanak C & Podder, N, 1976. "Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations," Econometrica, Econometric Society, vol. 44(1), pages 137-148, January.
    8. Satya Paul & Sriram Shankar, 2020. "An alternative single parameter functional form for Lorenz curve," Empirical Economics, Springer, vol. 59(3), pages 1393-1402, September.
    9. Kwang Soo Cheong, 2002. "An empirical comparison of alternative functional forms for the Lorenz curve," Applied Economics Letters, Taylor & Francis Journals, vol. 9(3), pages 171-176.
    10. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
    11. 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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