Atkinson Index
Also known as: Atkinson inequality measure, Atkinson's A, welfare-based inequality index
The Atkinson index is a welfare-based measure of inequality that incorporates an explicit, analyst-chosen parameter for how much society dislikes inequality. Introduced by Anthony Atkinson in 1970, it asks what fraction of total income could be discarded, under an equal distribution, while leaving social welfare unchanged — making the ethical judgement behind any inequality comparison transparent rather than hidden.
Key highlights
- Makes the ethical inequality-aversion judgement explicit and adjustable through the parameter epsilon.
- Has a direct welfare interpretation as the share of income society would forgo to eliminate inequality.
- Subgroup-decomposable, allowing between- and within-group inequality to be separated.
- By varying epsilon, can be made sensitive to whichever part of the distribution matters for the analysis.
Intuition
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How it works
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When to use it
Use the Atkinson index when you want an inequality measure whose normative content is explicit and tunable — to show how inequality comparisons depend on how much weight is placed on the poor, or to compute the welfare cost of inequality. It is the natural choice for welfare-economic and policy analysis and is subgroup-decomposable. It requires choosing the aversion parameter epsilon, which is a value judgement, not a statistical estimate; results should be reported across a range of epsilon. It is defined for positive incomes (zeros or negatives break the power mean for epsilon ≥ 1) and, like other scalar measures, can rank distributions whose Lorenz curves cross differently depending on epsilon.
Strengths & limitations
- Makes the ethical inequality-aversion judgement explicit and adjustable through the parameter epsilon.
- Has a direct welfare interpretation as the share of income society would forgo to eliminate inequality.
- Subgroup-decomposable, allowing between- and within-group inequality to be separated.
- By varying epsilon, can be made sensitive to whichever part of the distribution matters for the analysis.
- Requires the analyst to choose the aversion parameter, which is a normative rather than empirical decision.
- Defined only for positive incomes; zeros and negatives are problematic, especially for epsilon ≥ 1.
- Less familiar and intuitive to general audiences than the Gini coefficient.
- Different epsilon values can reverse the inequality ranking of distributions with crossing Lorenz curves.
Common pitfalls
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Applications
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Frequently asked
What does the inequality-aversion parameter epsilon control?
Epsilon sets how strongly the index weights the lower end of the distribution. At epsilon = 0 distribution is ignored and the index is zero; as epsilon increases, transfers to poorer people count for more and the same distribution registers as more unequal. Common reported values are 0.5, 1, and 2. Because epsilon encodes an ethical stance, best practice is to report the index across several values.
How is the Atkinson index interpreted as a welfare cost?
An Atkinson value of A means that society could achieve the same level of social welfare with only (1 − A) of its current mean income if that income were distributed perfectly equally — equivalently, inequality is 'wasting' a fraction A of potential welfare. So A = 0.25 says a quarter of income is, in welfare terms, lost to inequality at the chosen aversion level.
How does the Atkinson index relate to the generalized entropy and Gini measures?
The Atkinson index is ordinally equivalent to a member of the generalized entropy (Theil) family for each epsilon, so they rank distributions identically though on different scales, and both are subgroup-decomposable. Unlike the Gini, the Atkinson index has an explicit welfare parameter and clean subgroup decomposition; unlike the Gini's pairwise-difference interpretation, it is grounded in a social-welfare function.
Sources
- 1.Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2(3), 244–263.
- 2.Cowell, F. A. (2011). Measuring Inequality (3rd ed.). Oxford University Press.ISBN 978-0-19-959403-0
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Cite this page
ScholarGate. (2026, June 22). Atkinson Index. ScholarGate. https://scholargate.app/sociology/atkinson-index