polar.aff {affluenceIndex}R Documentation

Polarization index

Description

Computes the Wolfson polarization index.

Usage

polar.aff(x)

Arguments

x

the income vector

Details

Standard inequality measures do not give any information about polarization. A more polarized income distribution is one that has relatively fewer middle income class and more low- and/or high-income households (Alichi et al. 2016). Low income class is very often identified with poverty and high-income class with richness. One of the measures of polarization is the Wolfson polarization index given by (Wolfson 1994)

P= ≤ft(T-\frac{G}{2} \right) \frac{μ}{Me},

where T is the difference between 0.5 and the income share of bottom half of the population, G is the Gini coefficient, μ is the mean income, Me is the median income.
In order to have index from \langle 0,1 \rangle interval, Wolfson defined the scalar polarization index:

P^* = 2 ≤ft( 2T-G \right) \frac{μ}{Me}.

Value

gini

the Gini coefficient

p

the Wolfson polarization index

p.scalar

the Wolfson scalar polarization index

T

the difference between 0.5 and the income share of bottom half of the population

Author(s)

Alicja Wolny-Dominiak, Anna Sączewska-Piotrowska

References

1. Alichi A., Kantenga K., Solé J. (2016) Income polarization in the United States. IMF Working Paper, WP/16/121.
2. Wolfson M.C. (1994) When inequalities diverge, The American Economic Review, 84, pp. 353-358.

Examples

data(affluence)
polar.aff(affluence$income)

[Package affluenceIndex version 1.0 Index]