*! version 1.0 11jan2010
help gconc

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

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)

Zurab Sajaya (zsajaia at worldbank dot org)