Atkinson index edit
extracted from Wikipedia, the Free Encyclopedia (using Wikipedia Reflection Script)

 

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=1, \end{cases}

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

The entropy measure developped by Atkinson1 can be computed from a "normalized Theil index"2. This, however, only applies to the Theil index I1, which is derived from the "generalized entropy class"3 with ε = 1. The Atkinson index is computed using the function 1 − e − T.

Contents

See also

Footnotes

  1. ^ 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
  2. ^ Juana Domínguez-Domínguez, José Javier Núñez-Velázquez: The Evolution of Economic Inequality in the EU Countries During the Nineties. 2005
  3. ^ James E. Foster in annexe A.4.1 (p.142) of: Amartya Sen, On Economic Inequality, 1973/1997

References

External links

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