Estimating aversion to rank inequality underlying selected italian indices of income inequality
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In this paper, we estimate aversion to rank inequality (ATRI) underlying selected Italian income inequality indices, I, notably the Pietra index, the Bonferroni index and the “new” Zenga index. We measure ATRI by the parameter v of the generalised Gini index G(v). ATRI is distinct from aversion to income inequality, as measured by parameter ε of Atkinson’s index A(ε). We propose eliciting v from the equation I = GE(v). As, in general, an analytical solution to this equality can be cumbersome, we retrieve v from the empirical equation Iˆ = Gˆ (v) where the symbols Iˆ and Gˆ (v) denote the estimates of I and G(v), respectively. We also calculate the benchmark income x* such that adding a small income to it does not affect inequality. In this paper, we solve the equation using the estimates of the Italian inequality indices for Poland from 2000 to 2017. We have found, on average, v≈1.5 for the Pietra index, v ≈ 3 for the Bonferroni index, and v ≈ 11 for the Zenga index.
keywordsInequality, Inequality Aversion, Income Distribution, Benchmark IncomeAuthor biographyDepartment of Statistics and Econometrics - Gdansk University of Technology - Narutowicza 11/12 St. - 80-233 GDANSK - Poland (e-mail: skot@zie.pg.gda.pl.). |
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