help gconc-------------------------------------------------------------------------------

Title

gconc-- Generalized measures of concentraction

Syntax

gconcincomevar[outcomevar] [if] [in] [weight] [, nu(#)keepnegatives nozeros over(varlist)vce(vce_option) robustsvycluster(varlist})subpop(subpopspec)]

Description

gconccomputes 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 onlyincomevaris specified, the S-Gini coefficient is computed for this variable. If bothincomevarandoutcomevarare specified, then the coefficient of generalized concentration ofoutcomevarwith respect to ranking onincomevaris computed.

Options

optionsDescription -------------------------------------------------------------------------nu(#)The shape parameter for generalized concentration coefficient. The default value is 2 corresponding to the ranks ofincomevarentering linearly.

keepnegativesSpecifies whether the negative values ofincomevarare allowed.

nozerosSpecifies whether the zero values ofincomevarare 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.

robustRequests computation of the standard errors robust to heteroskedasticity inincomvar.

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

svyRequests estimation that respects complex sampling designs. The resampling variance estimatorssvy,vce(jackknife): gconc ...andsvy, 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,subpopoption should be specified to subset the data, rather thanifcondition. See[SVY] subpopulation estimation.

Notes and examplesTo compute Gini coefficient and its standard error:

. sysuse nlsw88. gconc wageTo compute Gini coefficient with the bootstrap standard error:

. sysuse nlsw88. bootstrap, reps(200): gconc wageTo compute concentration coefficient for complex survey data:

. webuse nhanes2. gconc height weight, svyTo compute concentration coefficient with the jackknife standard errors:

. webuse nhanes2. svy, vce(jackknife): gconc height weightExtensions of the Gini index that allow for different sensitivities in different parts of distribution were given by Yitzhaki (1983). Computations by

gconcutilize 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.

ReferencesBarrett, 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 Businessand 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 EconomicStatistics,9(2), 235--239, http://www.jstor.org/stable/1391792.

Also seeHelp: inequality, glcurve (if installed).

AuthorsStanislav Kolenikov (skolenik at gmail dot com)