S90S40: Palma index

In affluenceIndex: Affluence (Richness) Indices

Palma index

Description

Computes the Palma index (also known as S90/S40 ratio)

Usage

S90S40(x, weight)

Arguments

x	income vector
weight	vector of weights

Details

The Palma index is the ratio between the income share of the top 10\% and the bottom 40\%. The weighted Palma index (with weights w_1,w_2,...,w_n) is given by:

S90/S40 = \frac{\sum_{i=1}^n{x_iw_i}\boldsymbol{1}_{x_i>q_{w(0.9)}}}{\sum_{i=1}^n{x_iw_i}\boldsymbol{1}_{x_i \leq q_{w(0.4)}}},

where x_i is an income of individual i, n is the number of individuals, q_{w(0.9)},q_{w(0.4)} are the 0.9 and 0.4 quantiles, respectively, \boldsymbol{1}_{(\cdot)} denotes the indicator function, which is equal to 1 when its argument is true and 0 otherwise.

Value

S90S40

the value of index

Author(s)

Anna Saczewska-Piotrowska, Alicja Wolny-Dominiak

References

Cobham A., Sumner A.(2013). Is it all about the tails? The Palma measure of income inequality. Working Paper No. 343, Center for Global Development

affluenceIndex documentation built on Sept. 22, 2024, 1:06 a.m.