Under infinite variance, the Gini coefficient cannot be reliably estimated using conventional "non-parametric" methods. We study different approaches to the estimation of the Gini index in presence of a heavy tailed data generating process, that is, one with Paretan tails and/or in the stable distribution class with finite mean but non-finite variance ( with tail index \alpha\in(1,2)). While the Gini index is a measurement of fat tailedness, little attention has been brought to a significant downward bias in conventional applications, one that increases with lower values of \alpha. First, we show how the "non-parametric" estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution  as the data distribution shifts from the domain of attraction of a light tail distribution to the domain of attraction of a fat tailed, infinite variance one. Second, we show how the maximum likelihood estimator outperforms the non-parametric requiring a much smaller sample size to reach efficiency. Finally  we provide a simple correction mechanism to the small sample bias of the non-parametric estimator based on the distance between the mode and the mean of its asymptotic distribution for the case of heavy tailed data generating process .
 We study different approaches to the estimation of the Gini index in presence of a fat-tailed data generator process, i.e. one in the stable distribution class with finite mean but infinite variance (i.e. with tail index \alpha\in(1,2)). We show that, in such a case, the Gini coefficient can not be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges in case of fat tails. We start by discussing how the nonparametric estimator of the Gini index undergoes a phase transition in the symmetry structure of its asymptotic distribution , as the data distribution shifts from the domain of attraction of a light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We show how the nonparametric Gini bias increases with lower values of \alpha. We then prove that maximum likelihood estimation outperforms nonparametric methods, requiring a much smaller sample size to reach efficiency. Finally , for fat-tailed data, we provide a simple correction mechanism to the small sample bias of the nonparametric estimator based on the distance between the mode and the mean of its asymptotic distribution .
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Under infinite variance, the Gini coefficient cannot be reliably estimated using conventional "non-parametric" methods.
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heavy tailed data generating process, that is, one with Paretan tails and/or
fat-tailed data generator process, i.e. one
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non-finite variance (
infinite variance (i.e.
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While the Gini index is a measurement of fat tailedness, little attention has been brought to a significant downward bias in conventional applications, one that increases with lower values of \alpha. First, we show how the "non-parametric"
We show that, in such a case, the Gini coefficient can not be reliably estimated using conventional nonparametric methods, because of a downward bias that emerges in case of fat tails. We start by discussing how the nonparametric
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,
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light tail distribution to the domain of attraction of a fat tailed, infinite variance one. Second, we
light-tailed distribution to that of a fat-tailed one, especially in the case of infinite variance. We
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maximum likelihood estimator outperforms the non-parametric
nonparametric Gini bias increases with lower values of \alpha. We then prove that maximum likelihood estimation outperforms nonparametric methods,
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, for fat-tailed data,
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non-parametric
nonparametric
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for the case of heavy tailed data generating process