polar.aff {affluenceIndex} | R Documentation |
Computes the Wolfson polarization index.
polar.aff(x)
x |
the income vector |
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}.
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 |
Alicja Wolny-Dominiak, Anna Sączewska-Piotrowska
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.
data(affluence) polar.aff(affluence$income)