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QUADRATIC PEN's PARADES: SOME NEW RESULTS AND AN APPLICATION

Author

Listed:
  • Tomson Ogwang

    (Department of Economics, Brock University)

Abstract

In this paper we derive several new results with respect to the Gini index for a quadratic Pen's parade, building upon recent results by Mussard et al. (2011). To ensure that our results are relevant to many applied settings we impose only the parameter restrictions that guarantee the desirable property of convexity of the quadratic parade, which makes it in accord with the nature of many observed income distributions. We also account for the fact that the correlation between income and its rank is a function of the parameters of the parade. It turns out that for sufficiently large samples the reference value of the Gini index for a quadratic Pen's parade is 1/2. Whether the Gini index is equal to, less than or greater than 1/2 in these large sample situations depends on whether or not the quadratic parade passes through, above or below the origin, respectively. The problem of fitting a quadratic Pen's parade to observed income distributions is discussed and illustrated using Canadian data.

Suggested Citation

  • Tomson Ogwang, 2011. "QUADRATIC PEN's PARADES: SOME NEW RESULTS AND AN APPLICATION," Working Papers 1101, Brock University, Department of Economics, revised Dec 2011.
    • Handle: RePEc:brk:wpaper:1101
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    File URL: https://brocku.ca/repec/pdf/1101.pdf
    File Function: First version, March 2011
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    File URL: https://brocku.ca/repec/pdf/1101r.pdf
    File Function: Revised version, December 2011
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    Cited by:

    1. Sadefo Kamdem, Jules, 2012. "A nice estimation of Gini index and power Pen's parade," Economic Modelling, Elsevier, vol. 29(4), pages 1299-1304.

    More about this item

    Keywords

    Augmented Quadratic Pen’s Parade; Gini Index; Linear Pen’s Parade; Parsimonious Quadratic Pen’s Parade;
    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

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