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

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

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
unipersonal     nuclear    ampliado   compuesto coresidente 
  0.6143927   0.6166800   0.5014218   0.5729412   0.2584896 


$ws
$ws$wIntra
unipersonal     nuclear    ampliado   compuesto coresidente 
0.114476790 0.614083399 0.263965382 0.003540519 0.003933910 

$ws$sIntra
unipersonal     nuclear    ampliado   compuesto coresidente 
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"
       rentada       prestada propia_pagando         propia        litigio 
           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 1, 2019, 7:49 p.m.