Concept Architecture
Concept
Theoretically, the Atkinson Index is a measure of inequality that quantifies the proportion of total income or health that society would be willing to forgo in exchange for a perfectly equal distribution without reducing social welfare. It is founded on welfare economics and social welfare theory, incorporating explicit inequality aversion through a social welfare function. The concept exists to measure inequality while allowing the analyst to specify the degree of societal concern for inequality.
Mathematically, the Atkinson Index is derived from the equally distributed equivalent (EDE) level of income or health relative to the arithmetic mean. The index ranges from zero, representing perfect equality, to values approaching one as inequality increases. Its value depends on the inequality aversion parameter, with larger values placing greater weight on disparities among individuals with lower incomes or poorer health.
In practice, the Atkinson Index is estimated using individual-level data on income, health outcomes or health-related quality of life. In health economics it is applied to evaluate socioeconomic inequalities in health, assess the distributional effects of healthcare interventions and inform distributional cost-effectiveness analyses and equity-sensitive policy decisions.
Purpose
Used to quantify inequality while incorporating explicit societal preferences for equity, evaluate the distributional consequences of healthcare interventions, compare levels of health inequality across populations and support equity-informed resource allocation.
Mathematical Formulae
Primary Formula
For � ? 1:
A = 1 ? ((1/n) ????� x?^(1?�))^(1/(1?�)) / ?
where:
- A = Atkinson Index
- x? = income or health outcome for individual i
- n = number of individuals
- ? = arithmetic mean
- � = inequality aversion parameter
For � = 1:
A = 1 ? ((????� x?)^(1/n)) / ?
Supporting Formulae
Equally Distributed Equivalent (EDE):
EDE = ?(1 ? A)
Related Mathematical Methods
- Social Welfare Function
- Distributional Cost-Effectiveness Analysis
- Equally Distributed Equivalent (EDE)
- Inequality Aversion Modelling
- Equity Weighting
Example
Five individuals have health outcome values of 0.60, 0.70, 0.80, 0.90 and 1.00, with an inequality aversion parameter of 1.5.
The arithmetic mean health outcome is:
? = 0.80
Applying the Atkinson Index formula gives:
A � 0.049
This indicates that society would be willing to forgo approximately 4.9% of average health to achieve a perfectly equal distribution while maintaining the same level of social welfare.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| AVERAGE | =AVERAGE(B2:B6) | Calculates the mean health outcome or income. |
| POWER | =POWER(B2,1-$E$1) | Calculates transformed observations using the inequality aversion parameter. |
| SUM | =SUM(C2:C6) | Aggregates transformed values. |
| PRODUCT | =PRODUCT(B2:B6) | Calculates the geometric mean when � = 1. |
| POWER | =1-(POWER(AVERAGE(C2:C6),1/(1-$E$1))/AVERAGE(B2:B6)) | Calculates the Atkinson Index for � ? 1. |
VBA (Optional)
Automate calculation of the Atkinson Index across multiple populations and inequality aversion parameters to generate comparative equity analyses.
Sources
- Atkinson AB. On the Measurement of Inequality. Journal of Economic Theory. 1970.
- Atkinson AB. The Economics of Inequality.
- Cowell FA. Measuring Inequality.
- O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data.
- Asaria M, Griffin S, Cookson R. Distributional Cost-Effectiveness Analysis: A Tutorial. Health Economics.
Related Concepts (2)
Library
Publications
1
Fair Society, Healthy Lives: The Marmot Review (Strategic Review of Health Inequalities in England Post-2010) — Michael Marmot, Peter Goldblatt, Jessica Allen, et al., 2010 Edition ed., 2010 (The Marmot Review / UCL Institute of Health Equity)
The landmark strategic review of health inequalities in England, articulating the social determinants of health and the "social gradient" and setting out six policy objectives for reducing inequalities — the defining reference for health-inequalities policy in the UK.
Frequently Asked Questions (6)
What is the Atkinson index?
A measure of income or health inequality incorporating an explicit parameter reflecting society's aversion to inequality at the bottom of the distribution.
Source: Atkinson 1970
Who developed the Atkinson index?
The measure was proposed by Anthony Atkinson in 1970, who argued that any summary of inequality already embodies a value judgement about how much weight to give the worse off, and that this judgement should be made explicit rather than hidden. His index builds in a parameter representing aversion to inequality, so that the same distribution can yield different scores depending on how strongly low outcomes are weighted. This made the value basis of measurement transparent. Atkinson (1970) set out the approach.
Source: Atkinson 1970
How does the inequality-aversion parameter in the Atkinson index work?
The parameter expresses how much weight is given to inequality, and specifically to the bottom of the distribution: at zero, the index reflects no aversion and inequality is not penalised, while higher values place progressively more weight on the position of the worst off. As aversion rises, transfers from richer to poorer count for more in reducing the measured inequality. The parameter thus makes explicit a judgement that other inequality measures leave implicit or fixed.
Source: Atkinson 1970
How is the Atkinson index interpreted?
The index can be interpreted as the proportion of total income or health that could be given up, if the remainder were distributed equally, to achieve the same level of social welfare as the actual unequal distribution. A value of zero indicates complete equality, and higher values greater inequality, with the amount depending on the aversion parameter. This gives the measure a welfare interpretation, expressing inequality as the cost, in lost total, of the existing distribution.
Source: Atkinson 1970
How is the Atkinson index applied to health?
Applied to health, the Atkinson index measures inequality in a health outcome, such as life expectancy or a health-state score, across a population, with the aversion parameter expressing how much weight is placed on the health of the worst off. It allows the degree of concern about health inequality to be made explicit and varied, showing how the assessment changes as more weight is given to those in poorest health. This suits questions where the distribution of health, not only its average, matters.
Source: Atkinson 1970
What are the limitations of the Atkinson index?
The index requires choosing the aversion parameter, which is a value judgement rather than an empirical quantity, so the result depends on a parameter that reasonable people set differently, and no single value is correct. Applying it to health also requires health to be measured on a scale where the calculations are meaningful, which is demanding. Its welfare interpretation rests on assumptions about how individual health or income combine into social welfare that may be contested.
Source: Atkinson 1970
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 26 Aug 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/atkinson-index
- Term code
- HE-EE-HE-001
Stable URI · Machine-readable · Resolvable · CC BY 4.0