gini

Compute the Gini index of a set of observations.

%gini(dsn, var, weight=, _gini_=, method=, issorted=no, lib=WORK);

Arguments

• dsn : a dataset reference with continuous observations;
• var : variable of the input dataset dsn on which the Gini index will be computed;
• weight : (option) weight (frequencies), either a variable in dsn to use to weight the values of var, or a constant value; default: weight=1, i.e. it is not used;
• method : (option) method used to compute the Gini index; it can be: LAEKEN, or CANONICAL; default: LAEKEN, i.e. the formula used for computing the Gini index (which is 100* Gini coefficient) as:

  gini = 100 * (( 2 * swtvarcw - swt2var ) / ( swt * swtvar ) - 1)
  

• issorted : (option) boolean flag (yes/no) set when the input data is already sorted; default: issorted=no, and the input will be sorted;
• lib : (option) name of the input library; by default: empty, i.e. WORK is used.

Returns

_gini_ : name of the macro variable storing the value of the Gini index.

Examples

Considering the following datasets gini10_1:

Obs	x
A	2
A	2
A	2
B	3
B	3

and gini10_2;

Obs	x	w
A	2	3
B	3	2

both calls to the macro:

%let gini=;
%gini(gini10_1, x, _gini_=gini);
%gini(gini10_2, x, weight=w, _gini_=gini);

actually return the Gini index: gini=10.

Run macro %_example_gini for examples.

Note

The default LAEKEN method implements the approach of Alfons & Templ. In short, this means that the macro %gini runs the following DATA step over already sorted data:

DATA _null_;
    SET &lib..&dsn end=__last;
    retain swt swtvar swt2var swtvarcw ss 0;
    xwgh = &weight * &x;
    ss + 1;
    swt + &weight;
    swtvar + xwgh;
    swt2var + &weight * xwgh;
    swtvarcw + swt * xwgh;
    if __last then
    do;
        gini = 100 * (( 2 * swtvarcw - swt2var ) / ( swt * swtvar ) - 1);
        call symput("&_gini_",gini);
    end;
run;

References

1. Gastwirth, J. L. (1972). "The estimation of the Lorenz curve and Gini index", The Review of Economics and Statistics, 306-316.
2. Templ, M. and Alfons, A. (2011): "Variance Estimation of Indicators on Social Exclusion and Poverty using the R Package laeken".
3. Yitzhaki, S. and Schechtman, E. (2012): "More than a dozen alternative ways of spelling Gini".
4. Alfons, A. and Templ, M. (2014): "Estimation of social exclusion indicators from complex surveys: The R package laeken".
5. Creedy, J. (2015): "A note on computing the Gini inequality measure with weighted data".
6. Web link on Gini Coefficient of inequality.

See also

%income_components_gini.