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A nice estimation of Gini index and power Pen's parade

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  • Jules Sadefo-Kamdem

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

Under the assumption that an economic variable y such as income, is a power function of its rank among n individuals, we provide the coefficient of variation and the Gini index as functions of the power degree of the Pen's parade. In fact, knowing the power degree of the Pen's parade function, we obtain the coefficient of variation and a sharp analytical simple way to compute Gini index in terms of the power degree. Reciprocally, knowing, the coefficient of variation of a said variable, we can also provide the power degree of the corresponding Pen's parade, hence deducting its shape. Several examples are given to illustrate our methods. Special attention is given to countries' Gini indices of the World development indicators report 2009 (WDI 2009).

Suggested Citation

  • Jules Sadefo-Kamdem, 2012. "A nice estimation of Gini index and power Pen's parade," Post-Print hal-02901877, HAL.
    • Handle: RePEc:hal:journl:hal-02901877
    DOI: 10.1016/j.econmod.2012.03.015
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    References listed on IDEAS

    as
    1. Stéphane Mussard & J. Sadefo Kamdem & Françoise Seyte & Michel Terraza, 2011. "Quadratic Pen'S Parade And The Computation Of The Gini Index," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 57(3), pages 583-587, September.
    2. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
    3. World Bank, 2009. "World Development Indicators 2009," World Bank Publications - Books, The World Bank Group, number 4367.
    4. 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.
    5. Shalit, Haim & Yitzhaki, Shlomo, 1984. "Mean-Gini, Portfolio Theory, and the Pricing of Risky Assets," Journal of Finance, American Finance Association, vol. 39(5), pages 1449-1468, December.
    6. Tomson Ogwang, 2011. "QUADRATIC PEN's PARADES: SOME NEW RESULTS AND AN APPLICATION," Working Papers 1101, Brock University, Department of Economics, revised Dec 2011.
    7. Milanovic, Branko, 1997. "A simple way to calculate the Gini coefficient, and some implications," Economics Letters, Elsevier, vol. 56(1), pages 45-49, September.
    8. Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
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    Cited by:

    1. Shao-Hsun Keng & Peter F. Orazem, 2019. "Performance pay, the marriage market and rising income inequality in Taiwan," Review of Economics of the Household, Springer, vol. 17(3), pages 969-992, September.

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    More about this item

    Keywords

    Applied econometrics; Development economics; Gini index; Income inequality; Pen's parade; World development indicators;
    All these keywords.

    JEL classification:

    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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