the difference between 0.5 and the income share of bottom half of the population
Arguments
x
the income vector
weight
vector of weights
Author
Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska
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 (Wolfson 1994).
Weighted version of this index is given by:
$$P_w= 2 \left( 2T-G_w \right) \frac{\mu_w}{\rho_w},$$
where \(T\) is the difference between 0.5 and the income share of bottom half of the population, \(G_w\) is the Gini coefficient,
\(\mu_w\) is the mean income, \(\rho_w\) is the median income.
References
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.