dineq (version 0.1.0)

gini_decomp: Decomposition of the Gini coefficient

Description

Decomposes the Gini coefficient into population subgroups. Distinction is made by between and within group inequality and an overlap (interaction) term.

Usage

gini_decomp(x, z, weights = NULL)

Arguments

x

a numeric vector containing at least non-negative elements.

z

a factor containing the population sub groups.

weights

an optional vector of weights of x to be used in the computation of the decomposition. Should be NULL or a numeric vector.

Value

a list with the results of the decomposition and the parts used for the decomposition, containing the following components:

gini_decomp

a list containing the decomposition: gini_total (value of the gini coefficient of x), gini_within (value of within-group inequality), gini_between (value of between-group inequality) and gini_overlap (value of overlap in inequality)

gini_group

a list containing gini_group (the gini coefficients of the different subgroups) and gini_group_contribution(the contribution of the subgroups to the total within-group inequality: adds up to gini_within)

gini_decomp

a list containing the means of x: mean_total (value of the mean of x of all subgroups combined) and mean_group (value of the mean of x of the individual subgroups) inequality) and gini_between (value of between-group inequality)

share_groups

the distribution of the subgroups z

share_income_groups

the distribution of vector x by subgroups z

number_cases

a list containing the number of cases in total, by subgroup (weighted and unweighted): n_unweighted (total number of unweighted x), n_weighted (total number of weighted x), n_group_unweighted (number of unweighted x by subgroup z), n_group_unweighted (number of weighted x by subgroup z)

Details

The decomposition of the Gini coefficient by between and within group inequality. In most cases there is an overlap of the distribution of both groups. Consequence is that between and within group inequality doesn't add up to the total Gini coefficient. In those cases there is an overlap term. Also referred to as interaction effect.

Within group inequality is calculated by using the Gini coefficient for each sub group. Between group inequality by using the gini coefficient of the average of both sub groups.

References

Mookherjee, D. and A. Shorrocks (1982) A decomposition analysis of the trend in UK income inequality, Economic Journal, 92 (368), p. 886-902.

Cowell F. (2000) Measurement of Inequality. In Atkinson A. and Bourguignon F. (eds.) Handbook of Income Distribution. Amsterdam: Elsevier, p. 87-166.

See Also

mld_decomp

Examples

# NOT RUN {
#Decomposition of the gini coefficient by level of education using Mexican Income data set
data(mex_inc_2008)
education_decomp <- gini_decomp(x=mex_inc_2008$income,z=mex_inc_2008$education,
weights=mex_inc_2008$factor)

#complete output
education_decomp

#Selected output: decomposition into between- and within-group inequality and overlap (interaction)
education_decomp["gini_decomp"]

# }