Decomposition by Groups for Atkinson Index

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Description

Decomposes by population subgroups an Atkinson measure of inequality within a vector.

Usage

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decompAtkinson(x, z, w = NULL, epsilon = 1, decomp = "BDA", ELMO = TRUE)

Arguments

x

Numeric vector with non-negative values (strictly positive when epsilon=1).

z

Factor who determines the subgroups.

w

Numeric vector of sampling weigths (optional).

epsilon

Parameter of the Atkinson index (must be strictly positive).

decomp

Character string specifying the decomposition. It must be one of "BDA" for the Blackorby and alii (1985) decomposition or "DP" for the Das and Parikh (1982) 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 Atk (value of inequality index) and epsilon (value of parameter).

decomp

a list with components within (value of within-group inequality), between (value of between-group inequality), residual (value of residual inequality) and, if ELMO is TRUE, betweenELMO (value of maximum between-group inequality).

intra

a list with component AtkGroups (the subgroup values of inequality index).

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

Atkinson A.B. (1970) On the Measurement of Inequality. Journal of Economic Theory, 2, pp. 244-263.

Blackorby C., Donaldson D., Auersperg M. (1981) A new procedure for the measurement of inequality within and among population subgroups. Canadian Journal of Economics, 14, pp. 665-685.

Das T., Parikh A. (1982) Decomposition of Inequality Measures and a Comparative Analysis. Empirical Economics, 7(1-2), pp. 23-48.

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.

See Also

calcAtkinson

Examples

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data(hhbudgets)

decompAtkinson(hhbudgets[,"ingreso"], hhbudgets[,"estructura"], epsilon=3)
summary(hhbudgets[,"tenencia"]) # 35 NA's
summary(decompAtkinson(x=hhbudgets[,"transporte"], z=hhbudgets[,"tenencia"], w=hhbudgets[,"factor"], decomp="DP", ELMO=FALSE))
summary(decompAtkinson(x=hhbudgets[,"transporte"], z=hhbudgets[,"tenencia"], w=hhbudgets[,"factor"], decomp="DP", epsilon=0.25))