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help for svyatk                                Biewen and Jenkins (14 May 2005)
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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 (2003).

The program may also be used to calculate sampling variances in the case where
there are i.i.d. observations: see Biewen and Jenkins (2003).

A companion program, svygei, provides estimates of Generalized Entropy
inequality indices, using the same methods.

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 [pweight = xewght], psu(psu_id) 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 [pweight = xewght], psu(hh_id)

. 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 Frankfurt, Germany
<biewen@wiwi.uni-frankfurt.de>

Stephen P. Jenkins, ISER, University of Essex, U.K.
<stephenj@essex.ac.uk>

References

Biewen, M. and S.P. Jenkins 2003. Estimation of Generalized Entropy and
Atkinson indices from complex survey data. Working Paper 2003-11, Institute
for Social and Economic Research, University of Essex.
http://www.iser.essex.ac.uk/pubs/workpaps/pdf/2003-11.pdf, Oxford Bulletin
of Economics and Statistics, submitted.

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, [Su-Z] svy

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