Derivation of generalised Lorenz curve ordinates with unit record data [An update of glcurve for Stata 7]
glcurve7 varname [weight] [if exp] [in range] [, pvar(newvarname) glvar(newvarname) sortvar(varname) by(varname) split nograph replace lorenz atip(string) rtip(string) graph_options ]
aweights and fweights are allowed; see help weights.
Important notice: As of Oct. 2004, ^glcurve7^ is an outdated release of ^glcurve^ (available for Stata 7 users).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), glcurve7 draws 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). glcurve7 can 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 of varname, order of cumulation (set with the sortvar option), and normalisation (e.g. by the mean of varname). Alternatively glcurve7 with the lorenz, atip or rtip option 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 the split) options. It can also be made manually by 'stacking' the data (see stack).
pvar(pvarname) generates the variable pvarname containing the x-ordinates of the created curve.
glvar(glvarname) generates the variable glvarname containing the y-ordinates of the created curve.
sortvar(sname) specifies the sort variable. By default, the data are sorted (and cumulated) in ascending order of varname. If the sortvar option is specified, sorting and cumulation is in ascending order of variable sname.
by(groupvar) specifies that the ordinates are to be computed separately for each subgroups defined by groupvar. groupvar must be numeric.
split specifies that *a series of new variables* are created containing the ordinates for each subgroup specified by by(groupvar) split can not be used without by(). If split is specified, then the string glname in glvar(glname) (truncated after 4 characters) is used as a prefix to create new variables glname_X1, glname_X2,... (where X1, X2, ... are the values taken by groupvar).
nograph avoids the automatic display of a crude graph made out of the created variables. nograph is assumed if by() is specified without split.
replace allows the variables specified in glvar(glvarname) and pvar(pvarname) to be overwritten if they are already existing. Otherwise glvarname and pvarname must be new variable names.
lorenz requires 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) and atip(povline) require that the ordinates of TIP curves are computed instead of generalised Lorenz ordinates. povline specifies 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)) and rtip() draws 'relative' TIP curves (by cumulating max(1-(x/z),0)).
graph_options are standard graph, twoway options.
. 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)
Philippe VAN KERM <email@example.com> University of Namur, Department of Economics Rempart de la Vierge 8 B-5000 Namur, Belgium.
Stephen P. JENKINS <firstname.lastname@example.org> ISER, University of Essex Colchester CO4 3SQ, U.K.
Cowell, 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.
Manual: [R] lorenz STB: STB-49 sg107.1, STB-48 sg107 On-line: help for sumdist (if installed)