Sensitivity of inequality measures considering regressive transfers with fixed relative income distance

Rodolfo Hoffmann () and Diego Camargo Botassio ()
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Rodolfo Hoffmann: University of São Paulo
Diego Camargo Botassio: State University of Maringá

METRON, 2020, vol. 78, issue 3, No 2, 279-296

Abstract: Abstract Several authors have noted that different inequality measures have different sensitivity behaviors to transfers in different parts of the income distribution. To analyze this issue, the authors generally fix the absolute difference between the incomes of the persons involved in the transfer (the donor and the recipient). In this paper, we make three contributions to the literature. First, we analyze the sensitivity of several inequality measures while fixing the relative difference between the incomes. Second, we construct relative sensitivity curves to compare the behavior of the sensitivity of these measures. Third, we analyze how the change from fixing absolute distance to fixing relative distance between incomes affects the principle of aversion to downside inequality (ADI). Our results are different from those found in the literature. For example, when income has a log-normal distribution and we fix the ratio between incomes, the Gini index is more sensitive to changes near the median of the distribution and not near the mode, as noted by the authors who fix the absolute difference between incomes. We show that the ADI principle is more restricted when considering the ratio between incomes. For this new interpretation, Theil’s T index corresponds to the new “frontier” for the generalized entropy class of inequality indices (and not the squared coefficient of variation, which is the frontier when absolute income distance is used).

Keywords: Gini index; Mehran and Piesch indexes; Theil’s indexes; Pigou–Dalton principle; Aversion to downside inequality (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s40300-020-00189-z

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