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Derivation of generalised Lorenz curve ordinates with unit record data[An update ofglcurvefor Stata 7]

glcurve7varname[weight] [ifexp] [inrange] [,pvar(newvarname)glvar(newvarname)sortvar(varname)by(varname)splitnographreplacelorenzatip(string)rtip(string)graph_options]

aweights andfweights are allowed; see help weights.

Description

Important notice: As of Oct. 2004, ^glcurve7^ is an outdated release of ^glcurve^ (available for Stata 7 users). The up-to-date release is available for Stata 8 users as ^glcurve^ (available on the SSC archive and on the Stata Journal website).Given a variable

varname, call it x with c.d.f. F(x),glcurve7draws its Generalised Lorenz curve and/or generates two new variables containing the Generalised Lorenz ordinates for x, i.e. GL(p) at each p = F(x). For a population ordered in ascending order of x, a graph of GL(p) against p plots the cumulative total of x divided by population size, against cumulative population share. GL(1) = mean(x).glcurve7can also be used to derive many other related concepts such as Lorenz curves, concentration curves and 'Three Is of Poverty' (TIP) curves, with appropriate definition ofvarname, order of cumulation (set with thesortvaroption), and normalisation (e.g. by the mean ofvarname). Alternativelyglcurve7with thelorenz,atiporrtipoption can be used directly to draw the related Lorenz, concentration and TIP curves.Comparisons of pairs of distributions (and dominance checks) can be undertaken by using the

by()(with or without thesplit) options. It can also be made manually by 'stacking' the data (seestack).

Options

pvar(pvarname)generates the variablepvarnamecontaining the x-ordinates of the created curve.

glvar(glvarname)generates the variableglvarnamecontaining the y-ordinates of the created curve.

sortvar(sname)specifies the sort variable. By default, the data are sorted (and cumulated) in ascending order ofvarname. If thesortvaroption is specified, sorting and cumulation is in ascending order of variablesname.

by(groupvar)specifies that the ordinates are to be computed separately for each subgroups defined bygroupvar.groupvarmust be numeric.

splitspecifies that *a series of new variables* are created containing the ordinates for each subgroup specified byby(groupvar)splitcan not be used withoutby(). Ifsplitis specified, then the stringglnameinglvar(glname)(truncated after 4 characters) is used as a prefix to create new variablesglname_X1,glname_X2,... (where X1, X2, ... are the values taken bygroupvar).

nographavoids the automatic display of a crude graph made out of the created variables.nographis assumed ifby()is specified withoutsplit.

replaceallows the variables specified inglvar(glvarname)andpvar(pvarname)to be overwritten if they are already existing. Otherwiseglvarnameandpvarnamemust be new variable names.

lorenzrequires that the ordinates of the Lorenz curve are computed instead of generalised Lorenz ordinates. The Lorenz ordinates of variable x, L(p), are GL(p)/mean(x).

rtip(povline)andatip(povline)require that the ordinates of TIP curves are computed instead of generalised Lorenz ordinates.povlinespecifies the value of the poverty line: it can be either a numeric value taken as the poverty line for all observations or a variable name containing the value of the poverty line for each observation.atip()draws 'absolute' TIP curves (by cumulating max(z-x,0)) andrtip()draws 'relative' TIP curves (by cumulating max(1-(x/z),0)).

graph_optionsare standardgraph, twowayoptions.

Examples. glcurve7 x, gl(gl1) p(p1) nograph . graph gl1 p1, xlab ylab s(i) c(l)

. glcurve7 x [fw=wgt] if x > 0, gl(gl2) p(p2) lorenz

. glcurve7 x, gl(gl2) p(p2) replace sort(y) by(state) split

. glcurve7 x, gl(gl3) p(p3) atip(10000)

. glcurve7 x, gl(gl3) p(p3) atip(plinevar)

AuthorsPhilippe VAN KERM <philippe.vankerm@fundp.ac.be> University of Namur, Department of Economics Rempart de la Vierge 8 B-5000 Namur, Belgium.

Stephen P. JENKINS <stephenj@essex.ac.uk> ISER, University of Essex Colchester CO4 3SQ, U.K.

ReferencesCowell, F.A. (1995). Measuring Inequality (second edition). Prentice-Hall/Harvester-Wheatsheaf, Hemel Hempstead.

Jenkins, S.P. and Lambert, P.J. (1997). "Three 'I's of Poverty Curves, With An Analysis of UK Poverty Trends", Oxford Economic Papers, 49, 317-327.

Lambert, P.J. (1993). The Distribution and Redistribution of Income - A Mathematical Analysis. Second edition, Manchester University Press, Manchester and New York.

Shorrocks A.F. (1983). "Ranking Income Distributions", Economica, 197, 3-17.

Also seeManual:

[R] lorenzSTB:STB-49 sg107.1,STB-48 sg107On-line: help for sumdist (if installed)