Computes the measure of affluence analogous to the convex version of Foster, Greer and Thorbecke (1984) family of poverty indices.
r.fgt(x, weight, k, alpha)values of the sum in the index formula
the value of index
the income vector
vector of weights
multiple of the median income
parameter of the index: alpha > 1
Alicja Wolny-Dominiak, Anna Saczewska-Piotrowska
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.
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).
data(affluence)
r.fgt(affluence$income, weight = NULL, 2, 1)
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