{smcl}
{* 06Aug2017}{...}
{hline}
help for {hi:svygei}{right:Biewen and Jenkins (revised August 2017)}
{hline}
{title:Estimation of GE inequality indices from complex survey data}
{p 4 12}{cmd:svygei} {it:varname} [{cmd:if} {it:exp}]
[{cmd:in} {it:range}] [{cmd:,} {cmdab:a:lpha(}{it:#}{cmd:)}
{cmdab:sub:pop(}{it:varname}{cmd:)}
{cmdab:l:evel(}{it:#}{cmd:)}
{p}{cmd:svygei} typed without arguments redisplays the last estimates.
The level option may be used.
{p}The survey design variables must be set beforehand by {cmd:svyset},
see help {help svyset}.
{p}Warning: Use of {cmd:if} or {cmd:in} restrictions will not
produce correct variance estimates for subpopulations in many cases.
To compare estimates for subpopulations, use the {cmd:subpop()} option.
{title:Description}
{p}{cmd:svygei} provides estimates of finite-population
Generalised Entropy (GE) inequality indices, together with their
associated variance estimates. The GE class of inequality indices
is characterized by a sensitivity parameter, a. The program
calculates GE(a) for a = -1 and 2 plus the limiting cases
when a -> 0 (the mean logarithmic deviation, MLD) and when a -> 1
(the Theil index), and for one additional value (which defaults to
a = 3, unless set otherwise using the {cmd:alpha} option).
GE(2) is half the square of the coefficient of variation.
The indices differ in their sensitivities to differences
in different parts of the distribution of {it:varname}. The more
positive that a is, the more sensitive GE(a) is to differences
at the top of the distribution of varname; the more negative that
a is, the more sensitive it is to differences at the bottom of
the distribution of {it:varname}.
{p}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).
{p}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).
{p}A companion program, {cmd:svyatk}, provides estimates of Atkinson
inequality indices, using the same methods. For estimates of the Gini
Coefficient and Lorenz ordinates, see {cmd:svylorenz}.
{title:Options}
{p 0 4}{cmd:alpha} allows the user to choose a value of a (default = 3).
{p 0 4}{cmd:subpop({it:varname})} specifies that estimates be computed
for the single subpopulation defined by the observations for
which {it:varname}!=0. Typically, {it:varname}=1 defines the
subpopulation and {it:varname}=0 indicates observations not
belonging to the subpopulation. For observations whose
subpopulation status is uncertain, {it:varname} should be set to missing.
{title:Examples}
{p 8 12}{inp:. * (1) Income inequality among individuals using household survey data with obs = individual}
{p 8 12}{inp:. * weight = individual sample weight}
{p 8 12}{inp:. use income_ind, clear}
{p 8 12}{inp:. svyset psu_id [pweight = xewght], strata(strata_id) }
{p 8 12}{inp:. svygei income}
{p 8 12}{inp:. * (2) Income inequality among individuals using household survey data with obs = individual}
{p 8 12}{inp:. * weight = individual sample weight; survey PSU and strata not provided; household ID known}
{p 8 12}{inp:. use income_ind, clear}
{p 8 12}{inp:. svyset hh_id [pweight = xewght] }
{p 8 12}{inp:. svygei income}
{p 8 12}{inp:. * (3) Income inequality among individuals using survey data with obs = household; }
{p 8 12}{inp:. * all persons in same household have same income; survey PSU and strata not provided }
{p 8 12}{inp:. * weight = household weight x household size}
{p 8 12}{inp:. use income_hh, clear}
{p 8 12}{inp:. svyset [pweight = xhh_wt] }
{p 8 12}{inp:. svygei income}
{title:Authors}
{p 4 4}Martin Biewen, University of Tuebingen, Germany{break}
{p 4 4}Stephen P. Jenkins, London School of Economics, U.K.{break}
{title:Acknowledgement}
{p 4 4}After we released our program in 2005, the syntax for {cmd: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.
{title:References}
{p 4 4} Biewen, M. and S.P. Jenkins 2006. Variance estimation for Generalized
Entropy and Atkinson inequality indices: the complex survey data case.
{it: Oxford Bulletin of Economics and Statistics} 68: 371{c -}383 .
{p 4 4}Woodruff, R.S. 1971. A simple method for approximating the
variance of a complicated estimate.
{it:Journal of the American Statistical Association} 66: 411{c -}4.
{title:Also see}
{p 1 14}Manual: {hi:[U] 30 Overview of survey estimation}, {hi:[SVY]}{p_end}
{p 0 19}On-line: help for {help svy} and, if installed, {help svyatk},
{help geivars}, {help ineqdeco}, {help svylorenz}.{p_end}