Atkinson Profile

Atkinson Profile. The Atkinson Profile, more formally known as the Atkinson index, is a prominent measure of income inequality developed by the British economist Anthony B. Atkinson. It is a foundational tool in welfare economics that quantifies the degree of inequality within a given income distribution, incorporating explicit societal value judgments about aversion to inequality. Unlike simpler measures, it allows policymakers to weight the importance of transfers at different points in the distribution, making it a central concept in analyses of poverty and social justice.

Definition and Overview

The Atkinson Profile is defined as a family of indices derived from a social welfare function that is additively separable and isoelastic. Its core purpose is to measure the proportion of total income that could be foregone if the remaining income were equally distributed, while maintaining the same level of social welfare. This concept is deeply connected to the idea of the equally distributed equivalent income, a theoretical income level which, if received by every individual, would yield the same social welfare as the actual unequal distribution. The index's value ranges from 0, indicating perfect equality, to a maximum approaching 1, representing extreme inequality. Its development was a significant contribution to the field of public economics, providing a normative framework that bridges statistical measurement with ethical considerations about fairness.

Mathematical Formulation

Mathematically, the Atkinson index for a population is expressed as \( A_\varepsilon = 1 - \left( \frac{1}{N} \sum_{i=1}^N \left( \frac{y_i}{\bar{y}} \right)^{1-\varepsilon} \right)^{\frac{1}{1-\varepsilon}} \) for \( \varepsilon \neq 1 \), and as \( A_\varepsilon = 1 - \frac{\exp\left( \frac{1}{N} \sum_{i=1}^N \ln y_i \right)}{\bar{y}} \) for \( \varepsilon = 1 \). Here, \( y_i \) represents individual income, \( \bar{y} \) is the mean income, \( N \) is the population size, and \( \varepsilon \) is the key inequality aversion parameter. This parameter, central to the Atkinson index, reflects societal preferences: a value of zero implies indifference to inequality, while higher values indicate greater concern for the incomes of the poorest, drawing parallels with the weighting in a utilitarian framework. The formulation is closely related to the class of generalized entropy indices, with the Atkinson index being a monotonic transformation of the Theil index for certain parameter values.

Applications in Economics

The primary application of the Atkinson Profile is in the comparative analysis of income inequality across different countries, time periods, or policy regimes. Organizations like the World Bank, the OECD, and the Luxembourg Income Study frequently employ it in their flagship reports, such as the World Development Report. It is instrumental in evaluating the redistributive effects of taxation and government transfer payments, including programs like the SNAP or the Earned Income Tax Credit. Researchers use it to assess the impact of major economic events, such as the 2008 financial crisis or the implementation of NAFTA, on distributional outcomes. Its sensitivity parameter allows analysts to test how conclusions about inequality trends change under different ethical stances, informing debates within political economy.

Criticisms and Limitations

A major criticism of the Atkinson Profile is its dependence on the normative choice of the inequality aversion parameter \( \varepsilon \), which is inherently subjective and not directly observable. Different values can lead to contradictory rankings of distributions, a problem highlighted in discussions of Arrow's impossibility theorem. The index is also criticized for being more difficult to interpret intuitively than the Gini coefficient or the P90/P10 ratio. It satisfies the Pigou–Dalton principle of transfers but, like many summary measures, can be insensitive to changes at the very top or bottom of the distribution unless the aversion parameter is set extremely high. Furthermore, it typically requires complete and accurate microdata on incomes, which can be a limitation in studies of developing nations where data from national statistical offices may be sparse or unreliable.

Related Concepts

The Atkinson Profile is intrinsically linked to several other core measures and theories in inequality analysis. It is a specific member of the broader class of generalized entropy indices and is ordinally equivalent to the Theil index for certain parameters. Its theoretical foundation is the social welfare function, a concept advanced by economists like Abram Bergson and Paul Samuelson. It is often compared and contrasted with the Gini coefficient, the Hoover index, and the Lorenz curve, from which it can be derived. The underlying concept of equally distributed equivalent income relates to discussions of veil of ignorance reasoning in the work of John Rawls and John Harsanyi. In policy modeling, it is used alongside tools like microsimulation models to forecast the effects of legislation from bodies like the United States Congress or the European Parliament. Category:Economic indices Category:Welfare economics Category:Income distribution