r.fgt {affluenceIndex}R Documentation

Convex measure of affluence

Description

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

Usage

r.fgt(x, k, alpha)

Arguments

x

the income vector

k

multiple of the median income

alpha

parameter of the index: alpha > 1

Details

Peichl et. al (2008) defined an affluence index

R_{α}^{FGT,T2}(\mathbf{x},ρ)=\frac{1}{n} ∑_{i=1}^{n} ≤ft( ≤ft(\frac{x_i - ρ}{ρ} \right)_{+} \right)^{α},α>1,

where x_i is an income of individual i, n is the number of individuals, ρ is the richness line. Index satisfies transfer axiom T2 (convex): a richness index should decrease when a rank-preserving progressive transfer between two rich people takes place.

Value

r

values of the sum in the index formula

r.fgt

the value of index

Author(s)

Alicja Wolny-Dominiak

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$income, 2, 1)$r.fgt

[Package affluenceIndex version 1.0 Index]