IDEAS home Printed from https://ideas.repec.org/a/ebl/ecbull/eb-12-00636.html
   My bibliography  Save this article

Evaluation of the goodness of fit of new statistical size distributions with consideration of accurate income inequality estimation

Author

Listed:
  • Masato Okamoto

    (Ministry of Internal Affairs and Communications)

Abstract

This paper compares the goodness-of-fit of two new types of parametric income distribution models (PIDMs), the kappa-generalized (kG) and double-Pareto lognormal (dPLN) distributions, with that of beta-type PIDMs using US and Italian data for the 2000s. A three-parameter model kG tends to estimate the Lorenz curve and income inequality indices more accurately when the likelihood value is similar to that of the beta-type PIDMs. For the first half of the 2000s in the USA, the kG outperforms the other PIDMs in goodness-of-fit evaluated by both frequency-based criteria (such as the maximum likelihood value) and money-amount-based criteria (such as accuracy of estimation of the Lorenz curve). A four-parameter model dPLN generally outperforms the GB2 in both criteria. Furthermore, when the overall income distribution is approximated by a mixture of distributions fitted separately for each age class of the household heads (the ‘MLE-by-Age' method), the goodness-of-fit of the dPLN mixture model is found to be comparable to or higher than that of all of the PIDMs in the ordinary MLE fit, and, in the overall evaluation, this mixture model outperforms all of the single PIDMs in the sense that it is better fitted according to at least in one of the two criteria in almost all cases. The dPLN and its mixture model are found to have an explicit analytic expression for the Gini coefficient. The dPLN is therefore also suitable for the MLE-by-Age method in this respect.

Suggested Citation

  • 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.
    • Handle: RePEc:ebl:ecbull:eb-12-00636
    as

    Download full text from publisher

    File URL: http://www.accessecon.com/Pubs/EB/2012/Volume32/EB-12-V32-I4-P285.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. F. Clementi & M. Gallegati & G. Kaniadakis, 2009. "A k-generalized statistical mechanics approach to income analysis," Papers 0902.0075, arXiv.org, revised Feb 2009.
    2. F. Clementi & M. Gallegati & G. Kaniadakis, 2007. "κ-generalized statistics in personal income distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 187-193, May.
    3. 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.
    4. 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.
    5. Okamoto, Masato, 2012. "The Relationship between the Equivalence Scale and the Inequality Index and Its Impact on the Measurement of Income Inequality," MPRA Paper 37410, University Library of Munich, Germany.
    6. 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.
    7. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fabio CLEMENTI & Mauro GALLEGATI, 2017. "NEW ECONOMIC WINDOWS ON INCOME AND WEALTH: THE k-GENERALIZED FAMILY OF DISTRIBUTIONS," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 6(1), pages 1-15, JULY.
    2. Masato Okamoto, 2022. "Lorenz and Polarization Orderings of the Double-Pareto Lognormal Distribution and Other Size Distributions," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 548-574, November.
    3. 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.
    4. Masato Okamoto, 2014. "A flexible descriptive model for the size distribution of incomes," Economics Bulletin, AccessEcon, vol. 34(3), pages 1600-1610.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Masato Okamoto, 2014. "A flexible descriptive model for the size distribution of incomes," Economics Bulletin, AccessEcon, vol. 34(3), pages 1600-1610.
    3. 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.
    4. Sarabia, José María & Jordá, Vanesa, 2014. "Explicit expressions of the Pietra index for the generalized function for the size distribution of income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 582-595.
    5. 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.
    6. 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.
    7. 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.
    8. Bourguignon, Marcelo & Saulo, Helton & Fernandez, Rodrigo Nobre, 2016. "A new Pareto-type distribution with applications in reliability and income data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 166-175.
    9. Higbee, Joshua D. & Jensen, Jonathan E. & McDonald, James B., 2019. "The asymmetric log-Laplace distribution as a limiting case of the generalized beta distribution," Statistics & Probability Letters, Elsevier, vol. 151(C), pages 73-78.
    10. Fabio CLEMENTI & Mauro GALLEGATI, 2017. "NEW ECONOMIC WINDOWS ON INCOME AND WEALTH: THE k-GENERALIZED FAMILY OF DISTRIBUTIONS," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 6(1), pages 1-15, JULY.
    11. 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.
    12. 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.
    13. Saissi Hassani, Samir & Dionne, Georges, 2021. "The New International Regulation of Market Risk: Roles of VaR and CVaR in Model Validation," Working Papers 21-1, HEC Montreal, Canada Research Chair in Risk Management.
    14. Puente-Ajovin, Miguel & Ramos, Arturo, 2015. "An improvement over the normal distribution for log-growth rates of city sizes: Empirical evidence for France, Germany, Italy and Spain," MPRA Paper 67471, University Library of Munich, Germany.
    15. Dmitry I. Malakhov & Nikolay P. Pilnik & Igor G. Pospelov, 2015. "Stability of Distribution of Relative Sizes of Banks as an Argument for the Use of the Representative Agent Concept," HSE Working papers WP BRP 116/EC/2015, National Research University Higher School of Economics.
    16. Peter Grösche & Carsten Schröder, 2014. "On the redistributive effects of Germany’s feed-in tariff," Empirical Economics, Springer, vol. 46(4), pages 1339-1383, June.
    17. Alexander, Carol & Cordeiro, Gauss M. & Ortega, Edwin M.M. & Sarabia, José María, 2012. "Generalized beta-generated distributions," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1880-1897.
    18. Dorothée Boccanfuso & Bernard Decaluwé & Luc Savard, 2008. "Poverty, income distribution and CGE micro-simulation modeling: Does the functional form of distribution matter?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(2), pages 149-184, June.
    19. Kleiber, Christian, 1997. "The existence of population inequality measures," Economics Letters, Elsevier, vol. 57(1), pages 39-44, November.
    20. Erengul Dodd & George Streftaris, 2017. "Prediction of settlement delay in critical illness insurance claims by using the generalized beta of the second kind distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(2), pages 273-294, February.

    More about this item

    Keywords

    income distribution; mixture model; double-Pareto lognormal distribution; kappa-generalized distribution;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ebl:ecbull:eb-12-00636. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: John P. Conley (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.