IC2 (version 1.0-1)

decompSGini: Decomposition by Groups for Extended Gini Coefficient

Description

Decomposes by population subgroups the extended Gini coefficient of inequality within a vector.

Usage

decompSGini(x, z, w = NULL, param = 2, decomp = "BM", ELMO = TRUE)

Arguments

x

Numeric vector with non-negative values.

z

Factor who determines the subgroups.

w

Numeric vector of sampling weigths (optional).

param

Parameter specifying the extended Gini index (must be strictly positive).

decomp

Character string specifying the decomposition. This must be one of "BM" for the Bhattacharya and Mahalanobis (1967) decomposition or "YL" for the Yitzhaki and Lerman (1991) decomposition.

ELMO

When ELMO is TRUE, a "maximum" between-group inequality index is estimated using the Elbers and alii method (2005).

Value

A list of class "ICI" with components:

ineq

a list with components SGini (value of inequality index) and param (value of parameter).

decomp

a list with components within (value of within-group inequality), between (value of between-group inequality), overlap (value of residual inequality) when decomp = "BM" or stratif (value of residual inequality) when decomp = "YL" and, if ELMO is TRUE, betweenELMO (value of maximum between-group inequality).

intra

a list with components SGiniGroups (the subgroup values of inequality index) and contribSGiniGroups (the contribution of each subgroup to the total within-group inequality).

stratif

only if decomp = "YL", a list with components stratifGroups (the index of stratification for each subgroup) and contribStratifGroups (the contribution of each subgroup to the total stratification).

ws

a list with components wIntra (the subgroup weights) and sIntra (the subgroup shares of x).

nas

a list with NA counts, including components xNA, zNA, wNA and totalNA.

References

Bhattacharya N., Mahalanobis B. (1967) Regional disparities in household consumption in India. Journal of the American Statistical Association, 62 (317), pp. 143-161.

Cowell F.A. (2000) Measurement of Inequality. In Atkinson A.B., Bourguignon F. (Eds.) Handbook of Income Distribution. Amsterdam, Elsevier, Vol. 1, pp. 87-166.

Elbers C., Lanjouw P., Mistiaen J.A., Ozler B. (2005) Re-Interpreting Sub-Group Inequality Decompositions. World Bank, World Bank Policy Research Working Paper 3687, 42 p.

Schechtman E., Yitzhaki S. (2008) Calculating the Extended Gini Coefficient from Grouped Data: A Covariance Presentation. Bulletin of Statistics & Economics, 2(S08), pp. 64-69.

Yitzhaki S., Lerman R. (1991) Income Stratification and Income Inequality. Review of Income and Wealth, 37(3), pp. 313-.29.

See Also

calcSGini

Examples

data(hhbudgets)

decompSGini(x=hhbudgets[,"ingreso"], z=hhbudgets[,"estructura"], param=4)
decompSGini(x=hhbudgets[,"transporte"], z=hhbudgets[,"estructura"], w=hhbudgets[,"factor"], decomp="YL", ELMO=FALSE)
summary(decompSGini(x=hhbudgets[,"transporte"], z=hhbudgets[,"tenencia"], w=hhbudgets[,"factor"], param=1.5))