help for svyatkBiewen and Jenkins (revised August 2017)

Estimation of GE inequality indices from complex survey data

svyatk varname [if exp]
[in range] [, epsilon(#)
subpop(varname)
level(#)

svyatk typed without arguments redisplays the last estimates.
The level option may be used.

The survey design variables must be set beforehand by svyset,
see help svyset.

Warning: Use of if or in restrictions will not
produce correct variance estimates for subpopulations in many cases.
To compare estimates for subpopulations, use the subpop() option.

Description

svyatk provides estimates of finite-population
Atkinson inequality indices, together with their associated variance
estimates. The Atkinson class of inequality indices, A(e),
is characterized by a sensitivity parameter, e (`epsilon'), where e > 0.
The program calculates A(e) for e = 0.5, 1, 1.5, and 2, and for one
additional value (which defaults to e = 2.5, unless set otherwise
using the epsilon option). The larger that e is, the more
sensitive that A(e) becomes to differences at the bottom of
the distribution of varname.

Sampling variances are calculated using a method proposed by
Woodruff (1971). The derivations assume that the sample under
consideration is sufficiently large that a Taylor series
approximation to the index holds. For full details of the
derivation of the sampling variances, see Biewen and Jenkins
(2006).

The program may also be used to calculate sampling variances in the
case where there are i.i.d. observations: see Biewen and Jenkins (2006).

A companion program, svygei, provides estimates of Generalized
Entropy inequality indices, using the same methods. For estimates of the Gini
Coefficient and Lorenz ordinates, see svylorenz.

Options

epsilon allows the user to choose a value of e (default = 2.5).

subpop(varname) specifies that estimates be computed
for the single subpopulation defined by the observations for
which varname!=0. Typically, varname=1 defines the
subpopulation and varname=0 indicates observations not
belonging to the subpopulation. For observations whose
subpopulation status is uncertain, varname should be set to missing.

Examples

. * (1) Income inequality among individuals using household survey data with obs = individual

. * Weight = individual sample weight

. svyset psu_id [pweight = xewght], strata(strata_id)

. svyatk income

. * (2) Income inequality among individuals using household survey data with obs = individual

. * weight = individual sample weight; survey PSU and strata not provided; household ID known

. use income_ind, clear

. svyset hh_id [pweight = xewght]

. svygei income

. * (3) Income inequality among individuals using survey data with obs = household;

. * all persons in same household have same income; survey PSU and strata not provided

. * weight = household weight x household size

. use income_hh, clear

. svyset [pweight = xhh_wt]

. svyatk income

Authors

Martin Biewen, University of Tuebingen, Germany

<martin.biewen@uni-tuebingen.de>

Stephen P. Jenkins, London School of Economics, U.K.

<s.jenkins@lse.ac.uk>

Acknowledgement

After we released our program in 2005, the syntax for svyset changed.
Users could continue to use our program under version control. This update
makes this redundant. We thank Philipp Poppitz for updating the program
from version 8.2 to version 10.

References

Biewen, M. and S.P. Jenkins 2006. Variance estimation for Generalized
Entropy and Atkinson inequality indices: the complex survey data case.
Oxford Bulletin of Economics and Statistics 68: 371-383 .

Woodruff, R.S. 1971. A simple method for approximating the
variance of a complicated estimate.
Journal of the American Statistical Association 66: 411-4.

Also see

Manual: [U] 30 Overview of survey estimation, [SVY]

On-line: help for svy and, if installed, svygei,
geivars, ineqdeco, svylorenz.