# decompAtkinson: Decomposition by Groups for Atkinson Index In IC2: Inequality and Concentration Indices and Curves

## Description

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

## Usage

 `1` ```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.

`calcAtkinson`

## Examples

 ```1 2 3 4 5 6``` ```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)) ```

### Example output

```\$ineq
\$ineq\$index
Atk
0.6053387

\$ineq\$parameter
epsilon
3

\$decomp
\$decomp\$within
[1] 0.5954879

\$decomp\$between
[1] 0.02435238

\$decomp\$cross
[1] 0.01450155

\$decomp\$betweenELMO
[1] 0.5457692

\$intra
\$intra\$AtkGroups
0.6143927   0.6166800   0.5014218   0.5729412   0.2584896

\$ws
\$ws\$wIntra
0.114476790 0.614083399 0.263965382 0.003540519 0.003933910

\$ws\$sIntra
0.082922195 0.633804602 0.269302892 0.005557520 0.008412791

\$nas
\$nas\$xNA
[1] 0

\$nas\$zNA
[1] 0

\$nas\$wNA
NULL

\$nas\$totalNA
[1] 0

attr(,"class")
[1] "ICI"
501            432            159           1343             63
otra           NA's
9             35
Length  Class   Mode
0   NULL   NULL
Atk        epsilon
0.11435        0.25000

Decomposition (DP):
within     between    residual
1.1128e-01  3.0111e-03  6.5006e-05
betweenELMO
0.093282
```

IC2 documentation built on May 29, 2017, 10:05 a.m.