decompSGini: Decomposition by Groups for Extended Gini Coefficient

In IC2: Inequality and Concentration Indices and Curves

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))

Example output

$ineq
$ineq$index
    SGini 
0.6554641 

$ineq$parameter
param 
    4 


$decomp
$decomp$within
[1] 0.3089239

$decomp$between
[1] 0.09194278

$decomp$overlap
[1] 0.2545974

$decomp$betweenELMO
[1] 0.5513497


$intra
$intra$SGiniGroups
unipersonal     nuclear    ampliado   compuesto coresidente 
  0.6697002   0.6729860   0.5712567   0.6564818   0.3897706 

$intra$contribSGiniGroups
 unipersonal      nuclear     ampliado    compuesto  coresidente 
6.357241e-03 2.619321e-01 4.060872e-02 1.291727e-05 1.289952e-05 


$stratif
NULL

$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"
$ineq
$ineq$index
    SGini 
0.5013212 

$ineq$parameter
param 
    2 


$decomp
$decomp$within
[1] 0.4919235

$decomp$between
[1] 0.01580329

$decomp$stratif
[1] -0.006405562

$decomp$betweenELMO
NULL


$intra
$intra$SGiniGroups
unipersonal     nuclear    ampliado   compuesto coresidente 
  0.6220186   0.5088453   0.4180800   0.4383521   0.3704078 

$intra$contribSGiniGroups
unipersonal     nuclear    ampliado   compuesto coresidente 
0.048409037 0.326501211 0.112195569 0.002012960 0.002804679 


$stratif
$stratif$stratifGroups
unipersonal     nuclear    ampliado   compuesto coresidente 
-0.22294565  0.02255787  0.14480880  0.09716189  0.31910382 

$stratif$contribStratifGroups
  unipersonal       nuclear      ampliado     compuesto   coresidente 
 0.0095405503 -0.0028154302 -0.0120444804 -0.0001949031 -0.0008912987 


$ws
$ws$wIntra
unipersonal     nuclear    ampliado   compuesto coresidente 
0.116008709 0.617737310 0.258660022 0.003476593 0.004117366 

$ws$sIntra
unipersonal     nuclear    ampliado   compuesto coresidente 
0.077825702 0.641651224 0.268359098 0.004592109 0.007571867 


$nas
$nas$xNA
[1] 0

$nas$zNA
[1] 0

$nas$wNA
[1] 0

$nas$totalNA
[1] 0


attr(,"class")
[1] "ICI"
  SGini          param        
0.35229        1.50000        

Decomposition (BM):
  within   between   overlap  
0.128545  0.048091  0.175653  
betweenELMO  
    0.28307  

IC2 documentation built on May 1, 2019, 7:49 p.m.