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

Tomson Ogwang

No 1101, Working Papers from Brock University, Department of Economics

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.

Keywords: Augmented Quadratic Pen’s Parade; Gini Index; Linear Pen’s Parade; Parsimonious Quadratic Pen’s Parade (search for similar items in EconPapers)
JEL-codes: C81 D31 D63 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2011-03, Revised 2011-12
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https://brocku.ca/repec/pdf/1101.pdf First version, March 2011 (application/pdf)
https://brocku.ca/repec/pdf/1101r.pdf Revised version, December 2011 (application/pdf)
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