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| Atkinson index | |
|---|---|
| Name | Atkinson index |
| Introduced | 1970 |
| Developer | Sir Anthony B. Atkinson |
| Field | Welfare economics |
| Related | Gini coefficient, Lorenz curve, Theil index |
Atkinson index The Atkinson index is a measure of income inequality introduced by Sir Anthony B. Atkinson in 1970. It is widely used in comparative studies by researchers at institutions such as the World Bank, Organisation for Economic Co-operation and Development, International Monetary Fund, United Nations Development Programme, and national statistical offices including the United States Census Bureau and the Office for National Statistics (United Kingdom). The index is applied in analyses by scholars in universities like Harvard University, University of Chicago, London School of Economics, Massachusetts Institute of Technology, and University of Oxford and in reports by think tanks such as the Brookings Institution and the Institute for Fiscal Studies.
The Atkinson index is defined as a social welfare-based measure that reflects the proportion of total income that could be redistributed to achieve equality without reducing social welfare as judged by a specified inequality aversion parameter. It is grounded in the axiomatic tradition of Paul Samuelson, John Hicks, Amartya Sen, Kenneth Arrow, and Anthony Atkinson himself. The index connects normative judgments about inequality aversion—related to work by Amartya Sen and John Rawls—to empirical distributions collected by agencies such as the European Central Bank and the National Bureau of Economic Research.
For a population of n individuals with incomes y1,...,yn and an inequality aversion parameter ε ≥ 0, the Atkinson index A(ε) is defined via an equally-weighted social welfare function based on constant relative inequality aversion utility. For ε ≠ 1 the equally-distributed equivalent income E satisfies E = [ (1/n) Σ_i y_i^(1-ε) ]^(1/(1-ε)), producing A(ε) = 1 − E/μ where μ is mean income. For ε = 1 the limit case uses the geometric mean: E = exp[ (1/n) Σ_i ln y_i ], yielding A(1) = 1 − E/μ. This formulation relates directly to concepts in the work of Vilfredo Pareto on distributions, and to measures like the Gini coefficient and Theil index. The parameter ε maps to ethical positions discussed by John Rawls (high ε emphasizes the worst-off) and by Amartya Sen (trade-offs between equity and efficiency).
The Atkinson index satisfies key axioms shared with other inequality measures, including symmetry, population replication invariance, and mean independence, while explicitly incorporating a parameter capturing inequality aversion. As ε increases, the index places greater weight on lower incomes, echoing normative positions from John Rawls and empirical priorities in reports by Oxfam and United Nations agencies. For ε = 0 the index equals zero, reflecting indifference to inequality (raw mean income focus), while extreme ε approaches imply concentration on the poorest tail similar to criteria used in Millennium Development Goals and Sustainable Development Goals. The Atkinson index is decomposable by population subgroups in a manner useful for analysts at the World Bank and researchers affiliated with the International Labour Organization.
Empirical computation requires microdata from household surveys such as the Luxembourg Income Study, Current Population Survey, European Social Survey, Household, Income and Labour Dynamics in Australia, or administrative tax records used by revenue authorities like the Internal Revenue Service. Estimation procedures must account for sampling weights, top-coding, nonresponse, and survey design effects—issues addressed in methodological literature from United States Census Bureau technical reports and working papers from the National Bureau of Economic Research. Variance estimation can use bootstrapping, jackknife, or influence-function approaches developed in the econometrics literature by authors at Princeton University and Stanford University. When applied to grouped data, the index is estimated using interpolation techniques akin to methods used for the Lorenz curve estimation in studies by Simon Kuznets.
The Atkinson index has been applied in cross-country comparisons in reports by the Organisation for Economic Co-operation and Development and the World Bank; in fiscal incidence studies by the Institute for Fiscal Studies and the Brookings Institution; in welfare analyses at the United Nations Development Programme; and in national policy evaluations by ministries of finance in countries such as United Kingdom, United States, Canada, Australia, and Sweden. Empirical examples include assessments of tax-benefit systems, poverty-reduction programs evaluated by World Bank projects, and redistribution effects in research by scholars at Yale University and Columbia University. The index is also used in comparative historical work on inequality spanning periods analyzed in datasets from Maddison Project and Angus Maddison.
Critiques of the Atkinson index include sensitivity to the choice of the inequality aversion parameter ε, potential instability with small sample sizes or heavy top-coding common in tax data processed by agencies like the Internal Revenue Service, and challenges in interpreting absolute values across populations with different means—a concern emphasized in discussions at institutions such as the International Monetary Fund and the European Commission. Some commentators compare it unfavorably to decomposable measures like the Theil index for subgroup decomposition used by researchers at the United Nations and prefer nonparametric approaches promoted in work at the World Bank. Debates over normative content recall philosophical disputes involving John Rawls, Amartya Sen, and Gerald Debreu about welfare aggregation and interpersonal comparisons.
Category:Inequality measures