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On the asymptotic distribution of (generalized) Lorenz transvariation measures

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  • Teng Wah Leo

    () (St. Francis Xavier University)

Abstract

Abstract A common problem associated with evaluating dominance relationships between distribution functions and their moments is the lack of resolution regarding the direction of dominance as a result of the functions crossing, prevalent in empirical applications. This paper proposes a method of examining the difference between (Generalized) Lorenz curves over the entire support of the variables, an idea first proposed by Anderson and Leo (On providing a complete ordering of non-combinable alternative prospects. University of Toronto Discussion Paper, 2017) and formalized by Anderson et al. (Somewhere between utopia and dystopia: choosing from multiple incomparable prospect. University of Toronto Discussion Paper, 2017) for the case of stochastic dominance. The method provides a way of ordering all the (Generalized) Lorenz curves under consideration. The paper also provides the exact limit distribution of these associated measures, which in consequence of the results due to Politis and Romano (Ann Stat 22(4):2031–2050, 1994), permits inference via subsampling, in lieu of the crossing of empirical (Generalized) Lorenz curves. We show that due to the relationship between the Lorenz curve and the Gini coefficient, the same can be said of the latter. An example is provided to demonstrate its application.

Suggested Citation

  • Teng Wah Leo, 2017. "On the asymptotic distribution of (generalized) Lorenz transvariation measures," METRON, Springer;Sapienza Università di Roma, vol. 75(2), pages 195-213, August.
  • Handle: RePEc:spr:metron:v:75:y:2017:i:2:d:10.1007_s40300-017-0117-z
    DOI: 10.1007/s40300-017-0117-z
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    References listed on IDEAS

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    1. Suman Seth & Gaston Yalonetzky, 2016. "Has the world converged? A robust analysis of non-monetary bounded indicators," Working Papers 398, ECINEQ, Society for the Study of Economic Inequality.
    2. Oliver Linton & Thierry Post & Yoon‐Jae Whang, 2014. "Testing for the stochastic dominance efficiency of a given portfolio," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 59-74, June.
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    4. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    5. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    6. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 723-735.
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