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Approximate Bayesian computation for Lorenz curves from grouped data

Author

Listed:
  • Genya Kobayashi

    (Chiba University)

  • Kazuhiko Kakamu

    (Kobe University)

Abstract

This paper proposes a new Bayesian approach to estimate the Gini coefficient from the grouped data on the Lorenz curve. The proposed approach assumes a hypothetical income distribution and estimates the parameter by directly working on the likelihood function implied by the Lorenz curve of the income distribution from the grouped data. It inherits the advantages of two existing approaches through which the Gini coefficient can be estimated more accurately and a straightforward interpretation about the underlying income distribution is provided. Since the likelihood function is implicitly defined, the approximate Bayesian computational approach based on the sequential Monte Carlo method is adopted. The usefulness of the proposed approach is illustrated through the simulation study and the Japanese income data.

Suggested Citation

  • Genya Kobayashi & Kazuhiko Kakamu, 2019. "Approximate Bayesian computation for Lorenz curves from grouped data," Computational Statistics, Springer, vol. 34(1), pages 253-279, March.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:1:d:10.1007_s00180-018-0831-x
    DOI: 10.1007/s00180-018-0831-x
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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. 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.
    3. 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.
    4. repec:bla:revinw:v:37:y:1991:i:4:p:447-52 is not listed on IDEAS
    5. 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.
    6. Duangkamon Chotikapanich & William Griffiths, 2005. "Averaging Lorenz curves," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 3(1), pages 1-19, April.
    7. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    8. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    9. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    10. Maxime Lenormand & Franck Jabot & Guillaume Deffuant, 2013. "Adaptive approximate Bayesian computation for complex models," Computational Statistics, Springer, vol. 28(6), pages 2777-2796, December.
    11. James B. McDonald & Michael Ransom, 2008. "The Generalized Beta Distribution as a Model for the Distribution of Income: Estimation of Related Measures of Inequality," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 8, pages 147-166, Springer.
    12. P. Ortega & G. Martín & A. Fernández & M. Ladoux & A. García, 1991. "A New Functional Form For Estimating Lorenz Curves," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(4), pages 447-452, December.
    13. repec:dau:papers:123456789/5724 is not listed on IDEAS
    14. Villasenor, JoseA. & Arnold, Barry C., 1989. "Elliptical Lorenz curves," Journal of Econometrics, Elsevier, vol. 40(2), pages 327-338, February.
    15. 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.
    16. Paul Fearnhead & Dennis Prangle, 2012. "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(3), pages 419-474, June.
    17. Rasche, R H, et al, 1980. "Functional Forms for Estimating the Lorenz Curve: Comment," Econometrica, Econometric Society, vol. 48(4), pages 1061-1062, May.
    18. Hasegawa, Hikaru & Kozumi, Hideo, 2003. "Estimation of Lorenz curves: a Bayesian nonparametric approach," Journal of Econometrics, Elsevier, vol. 115(2), pages 277-291, August.
    19. 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.
    20. Sarabia, Jose Maria & Castillo, Enrique & Slottje, Daniel J., 2002. "Lorenz ordering between McDonald's generalized functions of the income size distribution," Economics Letters, Elsevier, vol. 75(2), pages 265-270, April.
    21. Kazuhiko Kakamu, 2016. "Simulation Studies Comparing Dagum and Singh–Maddala Income Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 593-605, December.
    22. José María Sarabia, 2008. "Parametric Lorenz Curves: Models and Applications," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 9, pages 167-190, Springer.
    23. Basmann, R. L. & Hayes, K. J. & Slottje, D. J. & Johnson, J. D., 1990. "A general functional form for approximating the Lorenz curve," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 77-90.
    24. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
    25. Mark A. Beaumont & Jean-Marie Cornuet & Jean-Michel Marin & Christian P. Robert, 2009. "Adaptive approximate Bayesian computation," Biometrika, Biometrika Trust, vol. 96(4), pages 983-990.
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    Cited by:

    1. Mathias Silva, 2023. "Parametric estimation of income distributions using grouped data: an Approximate Bayesian Computation approach [Working Papers / Documents de travail]," Working Papers hal-04066544, HAL.
    2. Mathias Silva, 2023. "Parametric models of income distributions integrating misreporting and non-response mechanisms," AMSE Working Papers 2311, Aix-Marseille School of Economics, France.
    3. Tatjana Miljkovic & Ying-Ju Chen, 2021. "A new computational approach for estimation of the Gini index based on grouped data," Computational Statistics, Springer, vol. 36(3), pages 2289-2311, September.

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