S90S40 {affluenceIndex}

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