Atkinson index

From Wikipedia, the free encyclopedia

The Atkinson index (also known as the Atkinson measure) is a measure of economic income inequality developed by Anthony Barnes Atkinson. The distinguishing feature of the Atkinson index is its ability to gauge movements in different segments of the income distribution.

The index can be turned into a normative measure by imposing a coefficient $\varepsilon$ to weight incomes. Greater weight can be placed on changes in a given portion of the income distribution by choosing $\varepsilon$ , the level of "inequality aversion", appropriately. The Atkinson index becomes more sensitive to changes at the lower end of the income distribution as $\varepsilon$ approaches 1. Conversely, as the level of inequality aversion falls (that is, as $\varepsilon$ approaches 0) the Atkinson becomes more sensitive to changes in the upper end of the income distribution.

The Atkinson index is defined as:

$A= \begin{cases} 1-\frac{1}{\mu}\left(\frac{1}{N}\sum_{i=1}^{N}y_{i}^{1-\varepsilon}\right)^{1/(1-\varepsilon)} & \mbox{for}\ \varepsilon \in \left[0,1\right) \\ 1-\frac{1}{\mu}\left(\prod_{i=1}^{N}y_{i}\right)^{1/N} & \mbox{for}\ \varepsilon=0, \end{cases}$

where $y i$ is individual income (i = 1, 2, ..., N) and $μ$ is the mean income.

The entropy measure developped by Atkinson^[1] can be computed from a "normalized Theil index"^[2]. This, however, only applies to the Theil index $I 1$ , which is derived from the "generalized entropy class"^[3] with $ε = 1$ . The Atkinson index is computed using the function $1 - e - T$ .

1 See also
2 Footnotes
3 References
4 External links

[edit] See also

Income inequality metrics

[edit] Footnotes

^ Anthony Barnes Atkinson developped various metrics. The Atkinson index which is related to the Theil index has been described by Lionnel Maugis in Inequality Measures in Mathematical Programming for the Air Traffic Flow Management Problem with En-Route Capacities (published on occasion of IFORS 96), 1996
^ Juana Domínguez-Domínguez, José Javier Núñez-Velázquez: The Evolution of Economic Inequality in the EU Countries During the Nineties. 2005
^ James E. Foster in annexe A.4.1 (p.142) of: Amartya Sen, On Economic Inequality, 1973/1997

[edit] References

Paul D. Allison, Measures of Inequality, American Sociological Review, 43 (December 1978), pp. 865-880, presents a technical discussion of the Atkinson measure's properties.
Amartya Sen, James E. Foster: On Economic Inequality, Oxford University Press, 1996 (Python script for a selection of formulas in the book)
Income Inequality, 1947-1998, from the United States Census Office.

[edit] External links

Software:
- Free Online Calculator computes the Gini Coefficient, plots the Lorenz curve, and computes many other measures of concentration for any dataset
- Free Calculator: Online and downloadable scripts (Python and Lua) for Atkinson, Gini, and Hoover inequalities
- Users of the R data analysis software can install the "ineq" package which allows for computation of a variety of inequality indices including Gini, Atkinson, Theil.
- A MATLAB Inequality Package, including code for computing Gini, Atkinson, Theil indexes and for plotting the Lorenz Curve. Many examples are available.

This Econometrics-related article is a stub. You can help Wikipedia by expanding it.

Featured MP3 :

Atkinson index - Related Items

Atkinson index

Atkinson index - In the news

© 2008 Netencyclo - Netencyclo Home - Terms of Service - Privacy Policy - Program Policies
Netencyclo, the Wikipedia mirror : the biggest multilingual free-content encyclopedia on the Internet. It uses material from the Wikipedia article Atkinson index. All Wikipedia content is licensed under the GNU Free Documentation License (see details). Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities.

- Atkinson index -