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help for alorenz                                             Joao Pedro Azevedo
Samuel Franco
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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

exact specifies that the exact p-value be computed.  This may take a long

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

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.

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)
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