------------------------------------------------------------------------------- help foralorenzJoao Pedro Azevedo Samuel Franco -------------------------------------------------------------------------------

Derivation of the Pen's Parade, Lorenz and Generalised Lorenz curve from the em> pirical distribution

alorenzdepvar[ifexp] [inrange] [weight] [ ,points(number)by(varname)order(varname)glgpgegomgoaangle45format(string)output(string)viewfullviewcomparebase(refcat)grname(string)results(string)select(string)mlabangle(string)mlabsize(string)mark(value 1...value n)marklabel(valuelabel 1...valuelabel n)markvar(varname(categorical))invertxdecreaseksmirnovexactnoisilytwoway_options]

pweights,fweightsandaweightsare allowed; see help weights. See help weight.

Description

alorenzderive and plot the Pen's Parade, Lorenz and Generalized Lorenz curve from the empirical distribution. In addition,alorenzallow user to retrive the data used to generate the curves, and implement first order stochastic dominance (Saposnik, 1981, 1983), second order stochastic dominance (Shorrocks, 1983), and the Lorenz dominance analysis of the distribution (Atkinson, 1970). Moreover, following Pigou-Dalton principles, demonstrated by Marshall & Olkin (1979),alorenzalso ranks two or more social states by analysing the Lorenz, Generalized Lorenz, and Pen's Parade.alorenzalso performs the two-sample Kolmogorov-Smirnov tests of the equality of distributions.

Options

points(#)sets the number of the distribution points. If the selected number of points is larger than the number of observations, alorenz will automatically adjust its value, and display a warning message. Default value 10.

by(groupvar)repeats the command for each group of observations for which the values of the variables in varlist are the same. Groupvar must be an integer variable.

order(varname)Selects an alternative variable the build the cumulative distribution. The default is the population.

glplot the Lorenz curve (cumulated share of var by cumulated share of the population).

gpplot the Pen's Parade curve (max value of each percentile).

geplot the Generalized Lorenz curve (cumulated mean of var by cumulated share of the population).

gomplot the mean of variabledepvaragainst the mean of variableorderas ordered by percentiles of the population by variableorder.

goaplot the cumulated mean of variabledepvaragainst the cumulated mean of variableorderas ordered by percentiles of the population by variableorder.

angle45specifies that a 45 degree angel line is to the ploted at the Lorenz Curve.

formatspecify the display format for variables. Default format %12.2f.

outputdesired name of the data file writes in comma-separated format.

viewspecifies that the tabels are to be viewed on the Stata display window.

fullviewspecifies that all the possible variables are to be displayed at the Stata window.

grname(string)specifies an alternative name of the figures.

select(string)select particular observations to be marked on the plot.

invertinvert the axis of the gl, gp, ge, gom or goa plots.

xdecreaseinvert the order the the x-axis, from increasing to decreasing.

base(refcat)sets the value of the comparation categoric group that defided the base group. If the base category was not definedalorenzwill use the first category.

mark(value 1...value n)select particular values to be marked on the plot.

marklabel(valuelabel 1...valuelabel n)set the label for the selected values to be marked on the plot.

markvar(varname (categorical))select the values of a particular categorical variable to be marked on the graph.

ksmirnovperforms two-sample Kolmogorov-Smirnov tests of the equality of distributions. For more information please see ksmirnov.

exactspecifies that the exact p-value be computed. This may take a long time if n > 50. For more information please see ksmirnov.

noisilydisplays on the Stata screen the results of the Kolmogorov-Smirnov tests.

compareAnalysis the first order stochastic dominance (Saposnik, 1981, 1983), second order stochastic dominance (Shorrocks, 1983), and the Lorenz dominance of the distribution (Atkinson, 1970).

twoway_optionsaccept any options other thanname()orby()documented in[G]twoway_options

Saved Results

max_:Pen's Parade.ac_prop_:Loren's Curve.ac_mean_:Generalized Loren's Curve.speso:Population.ac_speso:Cumulative Population.prop_pop:Distribution of population.ac_prop_pop:Cumulative distribution of population.prop_:percentage ofdepvarby percentile.

Stocastic Dominance analysis (Marshall & Olkin, 1979)

I :Lack of envy.IE:Lack of envy and preference for equity.CE:Preference for growth with equity.

Examples. alorenz y

. alorenz y [pw=weight]

. alorenz y [pw=weight], points(10)

. alorenz y [pw=weight], points(10) format(%12.0f) view

. alorenz y [pw=weight], points(10) output(tab) fullview

. alorenz y [pw=weight], points(10) format(%12.0f) fullview output(tab)

. alorenz y [pw=weight], points(100) view gl

. alorenz y [pw=weight], points(100) view gl ge

. alorenz y [pw=weight], points(100) view gl ge gp

. alorenz y [pw=weight], points(100) view gl ge gp angle45 format(%12.0f) output(tab)

. alorenz y [pw=weight], points(100) view gl ge gp angle45 format(%12.0f) output(tab) by(pais)

. alorenz y [pw=weight], points(10) compare base(1)

. alorenz y [pw=weight], points(10) compare base(4)

. alorenz y [pw=weight], points(100) gp select(country == India | country == Brazil | country == Peru | country == Mexico)

. alorenz y [pw=weight], points(100) gp order(x) select(country == India | country == Brazil | country == Peru | country == Mexico)

ReferencesAtkinson, A.B., 1970, "On the Measurement of Inequality", Journal of Economic Theory, 2: 244-63.

Dalton, H., 1920, "The Measurement of the Inequality of Incomes", Economic Journal, 30: 348-61.

Marshall, A.W. and I.Olkin, 1979, Inequalities: Theory of Majorization and Its Applications. In: Mathematics in Science and Engineering, V. 143. Academic Press.

Pigou, A.F., 1912, Wealth and Welfare, Macmillan, London.

Saposnik, R., 1981, "Rank-Dominance in Income Distribution" Public Choice, 36 pp147-151.

Saposnik, R., 1983, "On Evaluating Income Distributions: Rank Dominance, the Suppes-Sen Grading Principle of Justice and Pareto Optimality", Public Choice, 40: 329-36.

Shorrocks A.F., 1983, "Ranking Income Distributions", Economica, 50: 3-17.

AuthorsJoao Pedro Azevedo jazevedo@worldbank.org

Samuel Franco

AknowledgementsThe authors would like to thank Andres Castaneda, Viviane Sanfelice, Gabriel Facchini, and Amer Hasan for their valuable suggestions. The usual disclaimer applies.

alorenzuses the Stata user written command _pecats produced by J. Scott Long and Jeremy Freese.

Also seeManual:

[R] lorenzOnline: help for glcurve; inequal7; ineqdeco; ksmirnov; wbopendata(if installed)