Sensitivity of inequality measures considering regressive transfers with fixed relative income distance
- PDF / 498,870 Bytes
- 18 Pages / 439.37 x 666.142 pts Page_size
- 53 Downloads / 166 Views
Sensitivity of inequality measures considering regressive transfers with fixed relative income distance Rodolfo Hoffmann1 · Diego Camargo Botassio2 Received: 27 April 2020 / Accepted: 26 September 2020 © Sapienza Università di Roma 2020
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
B
Diego Camargo Botassio [email protected] Rodolfo Hoffmann [email protected]
1
Department of Economics, Administration and Sociology, University of São Paulo, Av. Pádua Dias, 11-Agronomia, Piracicaba, SP 13418-900, Brazil
2
Department of Economics, State University of Maringá, Av. Colombo, 5790-Vila Esperança, Maringá, PR 87020-270, Brazil
123
R. Hoffmann, D. C. Botassio
1 Introduction In this paper we consider only measures of the inequality of a distribution that do not change if the variable is multiplied by a positive scalar, that is, measures that are mean-independent or income-homogeneous of degree zero [4,7,24].1 Different inequality measures that satisfy the Pigou–Dalton principle of transfers do not necessarily provide the same ranking of distributions because the pairwise comparison of Lorenz curves does not provide a complete ranking when two curves intersect [10,21]. Additionally, several authors have noted that different inequality measures have different sensitivity behaviors; that is, some measures are more sensitive to transfers in one tail of the income distribution, while other measures are more sensitive to changes in the other tail. Meanwhile, some measures are more sensitive to changes in
Data Loading...
