r.cha: Concave measure of affluence

In affluenceIndex: Affluence (Richness) Indices

Concave measure of affluence

Description

Computes the measure of affluence analogous to the poverty index of Chakravarty (1983).

Usage

r.cha(x, weight, k, beta)

Arguments

x	the income vector
weight	vector of weights
k	multiple of the median income
beta	parameter of the index: beta > 0

Details

Peichl et. al (2008) defined an affluence index. Weighted index (with weights w_1,w_2,...,w_n) is given by:

R^{CHA}_{\beta}(\boldsymbol{x},\boldsymbol{w},\rho_w) = \frac{\sum_{i=1}^n(1-(\frac{\rho_w}{x_i})^\beta)\boldsymbol{1}_{x_i > \rho_w}w_i}{\sum_{i=1}^n{w_i}}, \beta > 0,

where x_i is an income of individual i, n is the number of individuals, \rho_w is the richness line, \boldsymbol{1}_{(\cdot)} denotes the indicator function, which is equal to 1 when its argument is true and 0 otherwise. Index satisfies transfer axiom T1 (concave): a richness index should increase when a rank-preserving progressive transfer between two rich individuals takes place.

Value

r	elements of the sum in the index formula
r.cha	the value of index

Author(s)

Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska

References

1. Chakravarty S.R. (1983) A new index of poverty. Mathematical Social Sciences, 6, pp. 307-313.
2. Peichl A., Schaefer T., Scheicher C. (2008) Measuring richness and poverty - A micro data application to Europe and Germany. IZA Discussion Paper No. 3790, Institute for the Study of Labor (IZA).

Examples

data(affluence)
r.cha(affluence$income, weight = NULL, 2, 2)

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