help gconc
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Title

    gconc -- Generalized measures of concentraction


Syntax

        gconc incomevar [outcomevar] [if] [in] [weight] [, nu(#)
                keepnegatives nozeros over(varlist) vce(vce_option) robust
                svy cluster(varlist}) subpop(subpopspec) ]



Description

    gconc computes generalized measures of inequality and concentration
    including Gini, generalized Gini (S-Gini) and concentration indices.
    Probability weights (pweights) and importance weights (iweights) are
    allowed.  If only incomevar is specified, the S-Gini coefficient is
    computed for this variable. If both incomevar and outcomevar are
    specified, then the coefficient of generalized concentration of
    outcomevar with respect to ranking on incomevar is computed.

Options


    options               Description
    -------------------------------------------------------------------------
    nu(#)                 The shape parameter for generalized concentration
                            coefficient.  The default value is 2
                            corresponding to the ranks of incomevar entering
                            linearly.

    keepnegatives         Specifies whether the negative values of incomevar
                            are allowed.

    nozeros               Specifies whether the zero values of incomevar are
                            allowed.  By default, they are used in
                            estimation.

    over(varlist)         Requests estimation for separate subgroups in the
                            sample.  Note that generalized measures of
                            concentration are not decomposable into subgroups
                            in the strict technical sense: the total
                            concentration is not equal to the sum of subgroup
                            concentrations plus the between group
                            concentration.

    vce(vce_option)       Specifies the method to compute standard errors.
                            See vce_option.

    robust                Requests computation of the standard errors robust
                            to heteroskedasticity in incomvar.

    cluster(varlist)      Requests computation of the standard errors robust
                            to intraclass correlation due to varlist.

    svy                   Requests estimation that respects complex sampling
                            designs. The resampling variance estimators svy,
                            vce(jackknife): gconc ... and svy, vce(brr):
                            gconc ... will work without this option.  The
                            linearized standard errors, svy, vce(linearized),
                            are not directly supported, but can be obtained
                            with this option.

    subpop(subpopspec)    For complex survey samples, subpop option should be
                            specified to subset the data, rather than if
                            condition.  See [SVY] subpopulation estimation.


Notes and examples

    To compute Gini coefficient and its standard error:

        . sysuse nlsw88
        . gconc wage

    To compute Gini coefficient with the bootstrap standard error:

        . sysuse nlsw88
        . bootstrap, reps(200): gconc wage

    To compute concentration coefficient for complex survey data:

        . webuse nhanes2
        . gconc height weight, svy

    To compute concentration coefficient with the jackknife standard errors:

        . webuse nhanes2
        . svy, vce(jackknife): gconc height weight

    Extensions of the Gini index that allow for different sensitivities in
    different parts of distribution were given by Yitzhaki (1983).
    Computations by gconc utilize the representations of the Gini method
    family of concentration measures given by Yitzhaki (1991).  Sandstrom,
    Wretman and Walden (1988) report that linearization variance estimator of
    the Gini coefficient was biased by a factor of 10 in their simulations,
    and recommend using jackknife estimator. Jackknife is also the preferred
    estimatior in Yitzhaki (1991). However results in Barrett and Donald
    (2009) showed quite accurate performance of the linearization estimator.


References

    Barrett, G. F., and Donald, S. G. (2009).  Statistical Inference with
        Generalized Gini Indices of Inequality, Poverty, and Welfare.
        Journal of Business and Economic Statistics, 27 (1), 1-17,
        doi:10.1198/jbes.2009.0001.

    Sandstrom, A., Wretman, J. H., and Walden, B. (1988). Variance Estimators
        of the Gini Coefficient: Probability Sampling.  Journal of Business
        and Economic Statistics, 6 (1), 113--119, 
        http://www.jstor.org/stable/1391424.

    Yitzhaki, S. (1983). On an extension of the Gini inequality index.
        International Economic Review, 24 (3), 617--628, doi:10.2307/2648789.

    Yitzhaki, S. (1991).  Calculating jackknife variance estimators for
        parameters of the gini method.  Journal of Business and Economic
        Statistics, 9 (2), 235--239, http://www.jstor.org/stable/1391792.


Also see

    Help:  inequality, glcurve (if installed).


Authors

    Stanislav Kolenikov (skolenik at gmail dot com)