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Parametric Lorenz Curves and the Modality of the Income Density Function

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  • Krause, Melanie

Abstract

Similar looking Lorenz Curves can imply very different income density functions and potentially lead to wrong policy implications regarding inequality. This paper derives a relation between a Lorenz Curve and the modality of its underlying income density: Given a parametric Lorenz Curve, it is the sign of its third derivative which indicates whether the density is unimodal or zeromodal (i.e. downward-sloping). Several single- parameter Lorenz Curves such as the Pareto, Chotikapanich and Rohde forms are associated with zeromodal densities. The paper contrasts these Lorenz Curves with the ones derived from the (unimodal) Lognormal density and the Weibull density, which, remarkably, can be zero- or unimodal depending on the parameter. A performance comparison of these five Lorenz Curves with Monte Carlo simulations and data from the UNU-WIDER World Income Inequality Database underlines the relevance of the theoretical result: Curve-fitting of decile data based on criteria such as mean squared error might lead to a Lorenz Curve implying an incorrectly-shaped density function. It is therefore important to take into account the modality when selecting a parametric Lorenz Curve. --

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Bibliographic Info

Paper provided by Verein für Socialpolitik / German Economic Association in its series Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century with number 67390.

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Date of creation: 2012
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Handle: RePEc:zbw:vfsc12:67390

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Web page: http://www.socialpolitik.org/
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Keywords: Lorenz Curve; Income Distribution; Modality; Inequality; Goodness of Fit;

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  1. Rohde, Nicholas, 2009. "An alternative functional form for estimating the Lorenz curve," Economics Letters, Elsevier, vol. 105(1), pages 61-63, October.
  2. Villasenor, JoseA. & Arnold, Barry C., 1989. "Elliptical Lorenz curves," Journal of Econometrics, Elsevier, vol. 40(2), pages 327-338, February.
  3. McDonald, James B, 1984. "Some Generalized Functions for the Size Distribution of Income," Econometrica, Econometric Society, vol. 52(3), pages 647-63, May.
  4. Hasegawa, Hikaru & Kozumi, Hideo, 2003. "Estimation of Lorenz curves: a Bayesian nonparametric approach," Journal of Econometrics, Elsevier, vol. 115(2), pages 277-291, August.
  5. Ana Castaneda & Javier Diaz-Gimenez & Jose-Victor Rios-Rull, 2003. "Accounting for the U.S. Earnings and Wealth Inequality," Journal of Political Economy, University of Chicago Press, vol. 111(4), pages 818-857, August.
  6. Kakwani, N C & Podder, N, 1973. "On the Estimation of Lorenz Curves from Grouped Observations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 278-92, June.
  7. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
  8. Christian Kleiber, 2007. "A Guide to the Dagum Distributions," Working papers 2007/23, Faculty of Business and Economics - University of Basel.
  9. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," NBER Working Papers 3541, National Bureau of Economic Research, Inc.
  10. Frank Cowell & Maria-Pia Victoria-Feser, 2007. "Robust stochastic dominance: A semi-parametric approach," Journal of Economic Inequality, Springer, vol. 5(1), pages 21-37, April.
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