Derivation of the Pen's Parade, Lorenz and Generalised Lorenz curve from the em > pirical distribution
alorenz depvar [if exp] [in range] [weight] [ , points(number) by(varname) order(varname) gl gp ge gom goa angle45 format(string) output(string) view fullview compare base(refcat) grname(string) results(string) select(string) mlabangle(string) mlabsize(string) mark(value 1 ... value n) marklabel(valuelabel 1...valuelabel n) markvar(varname (categorical)) invert xdecrease ksmirnov exact noisily twoway_options ]
pweights, fweights and aweights are allowed; see help weights. See help weight.
Description
alorenz derive and plot the Pen's Parade, Lorenz and Generalized Lorenz curve from the empirical distribution. In addition, alorenz allow 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), alorenz also ranks two or more social states by analysing the Lorenz, Generalized Lorenz, and Pen's Parade. alorenz also 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.
gl plot the Lorenz curve (cumulated share of var by cumulated share of the population).
gp plot the Pen's Parade curve (max value of each percentile).
ge plot the Generalized Lorenz curve (cumulated mean of var by cumulated share of the population).
gom plot the mean of variable depvar against the mean of variable order as ordered by percentiles of the population by variable order.
goa plot the cumulated mean of variable depvar against the cumulated mean of variable order as ordered by percentiles of the population by variable order.
angle45 specifies that a 45 degree angel line is to the ploted at the Lorenz Curve.
format specify the display format for variables. Default format %12.2f.
output desired name of the data file writes in comma-separated format.
view specifies that the tabels are to be viewed on the Stata display window.
fullview specifies 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.
invert invert the axis of the gl, gp, ge, gom or goa plots.
xdecrease invert 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 defined alorenz will 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.
ksmirnov performs two-sample Kolmogorov-Smirnov tests of the equality of distributions. For more information please see ksmirnov.
exact specifies that the exact p-value be computed. This may take a long time if n > 50. For more information please see ksmirnov.
noisily displays on the Stata screen the results of the Kolmogorov-Smirnov tests.
compare Analysis the first order stochastic dominance (Saposnik, 1981, 1983), second order stochastic dominance (Shorrocks, 1983), and the Lorenz dominance of the distribution (Atkinson, 1970).
twoway_options accept any options other than name() or by() 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 of depvar by 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)
References
Atkinson, 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.
Authors
Joao Pedro Azevedo jazevedo@worldbank.org
Samuel Franco
Aknowledgements
The authors would like to thank Andres Castaneda, Viviane Sanfelice, Gabriel Facchini, and Amer Hasan for their valuable suggestions. The usual disclaimer applies. alorenz uses the Stata user written command _pecats produced by J. Scott Long and Jeremy Freese.
Also see
Manual: [R] lorenz Online: help for glcurve; inequal7; ineqdeco; ksmirnov; wbopendata(if installed)