Atkinsonindeksi

Atkinsonindeksi, or the Atkinson index, is a measure of income inequality based on an axiomatic social welfare function that incorporates aversion to inequality. It reflects how evenly income could be distributed if a society preferred equality according to a specified level of inequality aversion, expressed by the parameter ε > 0.

For a population of n individuals with incomes y1, y2, ..., yn and mean μ, the Atkinson index is defined as

A(ε) = 1 − [ (1/n) Σ ( (yi/μ)^(1−ε) ) ]^(1/(1−ε)) for ε ≠ 1.

When ε = 1, the index is defined by a limit: A(1) = 1 − exp{ (1/n) Σ ln(yi/μ) }.

In both cases, incomes are typically assumed positive ( yi > 0 ), since the formulas involve logarithms or fractional powers of income relative to the mean.

Interpretation and properties: A(ε) equals the proportional reduction in mean income that would be required to restore equality under the chosen aversion to inequality. It ranges from 0 (perfect equality) toward 1 in principle, with higher values indicating greater inequality. The parameter ε governs sensitivity to the lower end of the income distribution: larger ε gives more weight to poorer individuals, while smaller ε yields less sensitivity. The index is scale-invariant, so multiplying all incomes by a positive constant does not change A.

Uses and limitations: The Atkinson index is widely used in distributional analysis and cross-country comparisons, allowing researchers to tailor the measure to policy preferences by selecting ε. A limitation is its dependence on the chosen ε, which can influence rankings; it also requires careful handling of zero or extremely low incomes in empirical data.