r.fgt: Convex measure of affluence

In affluenceIndex: Affluence (Richness) Indices

Convex measure of affluence

Description

Computes the measure of affluence analogous to the convex version of Foster, Greer and Thorbecke (1984) family of poverty indices.

Usage

r.fgt(x, weight, k, alpha)

Arguments

x	the income vector
weight	vector of weights
k	multiple of the median income
alpha	parameter of the index: alpha > 1

Details

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

R_{\alpha}^{FGT,T2}(\mathbf{x},\mathbf{w},\rho_w)=\frac{\sum_{i=1}^{n} \left( \frac{x_i - \rho_w}{\rho_w}\right)^{\alpha}\mathbf{1}_{x_i>\rho_w}w_i}{\sum_{i=1}^{n}w_i},\alpha>1,

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 T2 (convex): a richness index should decrease when a rank-preserving progressive transfer between two rich individuals takes place.

Value

r	values of the sum in the index formula
r.fgt	the value of index

Author(s)

Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska

References

1. Foster J.E., Greer J., Thorbecke E. (1984) A class of decomposable poverty measures. Econometrica, 52, pp. 761-766.
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.fgt(affluence$income, weight = NULL, 2, 1)

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