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New Four- and Five-Parameter Models for Income Distributions

In: Modeling Income Distributions and Lorenz Curves

Author

Listed:
  • William J. Reed

    (University of Victoria)

  • Fan Wu

    (University of Victoria)

Abstract

Two parametric models for income distributions are introduced. The models fitted to log(income) are the 4-parameter normal-Laplace (NL) and the 5-parameter generalized normal-Laplace (GNL) distributions. The NL model for log(income) is equivalent to the double-Pareto lognormal (dPlN) distribution applied to income itself. Definitions and properties are presented along with methods for maximum likelihood estimation of parameters. Both models along with 4- and 5-parameter beta distributions, are fitted to nine empirical distributions of family income. In all cases the 4-parameter NL distribution fits better than the 5-parameter generalized beta distribution. The 5-parameter GNL distribution provides an even better fit. However fitting of the GNL is numerically slow, since there are no closed-form expressions for its density or cumulative distribution functions. Given that a fairly recent study involving 83 empirical income distributions (including the nine used in this paper) found the 5-parameter beta distribution to be the best fitting, the results would suggest that the NL be seriously considered as a parametric model for income distributions.

Suggested Citation

  • William J. Reed & Fan Wu, 2008. "New Four- and Five-Parameter Models for Income Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 11, pages 211-223, Springer.
    • Handle: RePEc:spr:esichp:978-0-387-72796-7_11
    DOI: 10.1007/978-0-387-72796-7_11
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    Citations

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    Cited by:

    1. Hajargasht, Gholamreza & Griffiths, William E., 2013. "Pareto–lognormal distributions: Inequality, poverty, and estimation from grouped income data," Economic Modelling, Elsevier, vol. 33(C), pages 593-604.
    2. Gholamreza Hajargasht and William E. Griffiths, 2012. "Pareto-Lognormal Income Distributions:Inequality and Poverty Measures, Estimation and Performance," Department of Economics - Working Papers Series 1149, The University of Melbourne.
    3. Walter, Paul & Weimer, Katja, 2018. "Estimating poverty and inequality indicators using interval censored income data from the German microcensus," Discussion Papers 2018/10, Free University Berlin, School of Business & Economics.
    4. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    5. James B. Mcdonald & Jeff Sorensen & Patrick A. Turley, 2013. "Skewness And Kurtosis Properties Of Income Distribution Models," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 59(2), pages 360-374, June.
    6. Boccanfuso, Dorothée & Richard, Patrick & Savard, Luc, 2013. "Parametric and nonparametric income distribution estimators in CGE micro-simulation modeling," Economic Modelling, Elsevier, vol. 35(C), pages 892-899.
    7. Toda, Alexis Akira, 2012. "The double power law in income distribution: Explanations and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 84(1), pages 364-381.
    8. Masato Okamoto, 2012. "Evaluation of the goodness of fit of new statistical size distributions with consideration of accurate income inequality estimation," Economics Bulletin, AccessEcon, vol. 32(4), pages 2969-2982.
    9. Callealta Barroso, Francisco Javier & García-Pérez, Carmelo & Prieto-Alaiz, Mercedes, 2020. "Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries," Economic Modelling, Elsevier, vol. 89(C), pages 512-522.
    10. Tetsugen HARUYAMA, 2021. "A Schumpeterian Exploration of Gini and Top/Bottom Income Shares," Discussion Papers 2125, Graduate School of Economics, Kobe University.
    11. Masato Okamoto, 2013. "Extension of the κ-generalized distribution: new four-parameter models for the size distribution of income and consumption," LIS Working papers 600, LIS Cross-National Data Center in Luxembourg.
    12. Masato Okamoto, 2014. "A flexible descriptive model for the size distribution of incomes," Economics Bulletin, AccessEcon, vol. 34(3), pages 1600-1610.
    13. Johan Fellman, 2021. "Aspects of Pareto distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 10(1), pages 1-4.

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