Atkinson index

With Atkinson measure ( according to Anthony Atkinson [ * 1944 ] ) are a set of inequality measures referred to, with which, for example, income or wealth inequality can be calculated in a society.

Origin / history

Introduced by Hugh Dalton Dalton- index is not invariant to positive linear transformations of the personal income welfare functions.

Atkinson in 1970 attempted to define the index so new that it has the appropriate invariance.

Definition

Each Atkinson measure is based on a concave utility function. How strongly reacts the Atkinson measure on inequality is determined by the underlying utility function.

Usually, an Arrow- welfare function is used, indicating by an inequality aversion parameter determines how large is the welfare difference of an additional Euros between a person with a high and a low income. The bigger epsilon, the stronger the degree Atkinson reacted for inequality. Is this means that the distribution of income is seen socially irrelevant.

Atkinson this index is defined as follows:

With individual income (i = 1, 2, ..., N) and the average income is.

Properties

The Atkinson index has the following properties:

, Where the number of sub-groups indicating the average income of the subgroup, and the weights for independent from the concrete situation the function f

Application

For which the " generalized entropy class" from the resulting Theil index with that it can be converted to a system developed by Atkinson entropy, which appeared in the literature as " normalized Theil index ". The measure is calculated from the function.