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
to weight incomes. Greater weight can be placed on changes in a
given portion of the income distribution by choosing ,
the level of "inequality aversion", appropriately. The Atkinson
index becomes more sensitive to changes at the lower end of the
income distribution as
approaches 1. Conversely, as the level of inequality aversion falls
(that is, as
approaches 0) the Atkinson becomes more sensitive to changes in the
upper end of the income distribution.
The Atkinson index is defined as:
where y_{i} is
individual income (i = 1, 2, ..., N) and μ is the mean income.
The entropy measure developed 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}.
See also
- ^
Anthony Barnes Atkinson developed 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
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.
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.