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Income inequality decomposition using a finite mixture of log-normal distributions: A Bayesian approach

Author

Listed:
  • Michel Lubrano

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Abdoul Aziz Junior Ndoye

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

The log-normal distribution is convenient for modelling the income distribution, and it offers an analytical expression for most inequality indices that depends only on the shape parameter of the associated Lorenz curve. A decomposable inequality index can be implemented in the framework of a finite mixture of log-normal distributions so that overall inequality can be decomposed into within-subgroup and between-subgroup components. Using a Bayesian approach and a Gibbs sampler, a Rao-Blackwellization can improve inference results on decomposable income inequality indices. The very nature of the economic question can provide prior information so as to distinguish between the income groups and construct an asymmetric prior density which can reduce label switching. Data from the \UK\ Family Expenditure Survey (FES) (1979 to 1996) are used in an extended empirical application.

Suggested Citation

  • Michel Lubrano & Abdoul Aziz Junior Ndoye, 2016. "Income inequality decomposition using a finite mixture of log-normal distributions: A Bayesian approach," Post-Print hal-01440303, HAL.
    • Handle: RePEc:hal:journl:hal-01440303
    DOI: 10.1016/j.csda.2014.10.009
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    Cited by:

    1. Ellis Scharfenaker, Markus P.A. Schneider, 2019. "Labor Market Segmentation and the Distribution of Income: New Evidence from Internal Census Bureau Data," Working Paper Series, Department of Economics, University of Utah 2019_08, University of Utah, Department of Economics.
    2. El Moctar Laghlal & Abdoul Aziz Junior Ndoye, 2018. "A Hybrid MCMC Sampler for Unconditional Quantile Based on Influence Function," Econometrics, MDPI, vol. 6(2), pages 1-11, May.
    3. Edwin Fourrier-Nicolaï & Michel Lubrano, 2021. "Bayesian Inference for Parametric Growth Incidence Curves," Research on Economic Inequality, in: Research on Economic Inequality: Poverty, Inequality and Shocks, volume 29, pages 31-55, Emerald Group Publishing Limited.
    4. Kazuhiko Kakamu, 2022. "Bayesian analysis of mixtures of lognormal distribution with an unknown number of components from grouped data," Papers 2210.05115, arXiv.org, revised Oct 2025.
    5. Majda Benzidia & Michel Lubrano, 2016. "A Bayesian Look at American Academic Wages: The Case of Michigan State University," AMSE Working Papers 1628, Aix-Marseille School of Economics, France.
    6. Edwin Fourrier-Nicolaï & Michel Lubrano, 2020. "Bayesian inference for TIP curves: an application to child poverty in Germany," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 18(1), pages 91-111, March.
    7. Yuki Kawakubo & Kazuhiko Kakamu, 2025. "Multilevel Decomposition of Generalized Entropy Measures Using Constrained Bayes Estimation: An Application to Japanese Regional Data," Papers 2506.21213, arXiv.org.
    8. Gregor Zens, 2018. "Bayesian shrinkage in mixture of experts models: Identifying robust determinants of class membership," Papers 1809.04853, arXiv.org, revised Jan 2019.
    9. Michel Lubrano & Zhou Xun, 2023. "The Bayesian approach to poverty measurement," Chapters, in: Jacques Silber (ed.), Research Handbook on Measuring Poverty and Deprivation, chapter 44, pages 475-487, Edward Elgar Publishing.
    10. Muhammad Hilmi Abdul Majid & Kamarulzaman Ibrahim & Nurulkamal Masseran, 2023. "Three-Part Composite Pareto Modelling for Income Distribution in Malaysia," Mathematics, MDPI, vol. 11(13), pages 1-15, June.
    11. Gregor Zens, 2019. "Bayesian shrinkage in mixture-of-experts models: identifying robust determinants of class membership," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 1019-1051, December.
    12. Nartikoev, Alan & Peresetsky, Anatoly, 2020. "Эндогенная Классификация Домохозяйств В Регионах России [Endogenous household classification: Russian regions]," MPRA Paper 104351, University Library of Munich, Germany.
    13. Aldo Gardini & Enrico Fabrizi & Carlo Trivisano, 2022. "Poverty and inequality mapping based on a unit‐level log‐normal mixture model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2073-2096, October.

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