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]