polar.aff: Wolfson polarization index
In affluenceIndex: Affluence (Richness) Indices

Description Usage Arguments Details Value Author(s) References Examples

Computes the Wolfson polarization index.

1	polar.aff(x, weight)

`x`	the income vector
`weight`	vector of weights

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 (Wolfson 1994). Weighted version of this index is given by:

P_w= 2 ≤ft( 2T-G_w \right) \frac{μ_w}{ρ_w},

where T is the difference between 0.5 and the income share of bottom half of the population, G_w is the Gini coefficient, μ_w is the mean income, ρ_w is the median income.

`Pw`	the value of index
`TT`	the difference between 0.5 and the income share of bottom half of the population

Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska

1. Alichi A., Kantenga K., Sole 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.