------------------------------------------------------------------------------- help forainequalJoao Pedro Azevedo -------------------------------------------------------------------------------

Measures of inequality (revised)

ainequalvarlist[weight] [ifexp] [inrange] [,format(%fmt)ATKinsonEPSilon(#[ #[ ...]])RELSGiniDelta(#[ #[ ...]])shorrocksalpha(#[ #[ ...]])nogininotheilrmdcovsdlmehranpieschkakwanimldge_1ge2allbenchmark]

aweights andfweights are allowed; see help weights.

Description

ainequalcomputes a series of inequality measures of the variables invarlist. It is a revised and upgraded version ofinequal7andinequalpublished by Edward Whitehouse in STB-23.The inequality measures computed are: the "relative mean deviation", the "coefficient of variation", the "standard deviation of logs", the"Gini index", the "Mehran index", the "Piesch index", the "Kakwani index", "Theil entropy index", the "mean log deviation", the "generalised entropy measure" for all sensitivity [see, e.g., Cowell [1995] and Amiel and Cowell [1999] for a definition of these measures], the "Atkinson Inequality Index" using the inequality aversion parameter epslon, and the "Donaldson-Weymark relative S-Gini" using the distributional sensitivity paramether delta.

In addition

ainequalalso computes the relative poverty line proposed by Hoffmann [2001] and Lambert and Lanza [2006], for the Gini, Theil-T and Theil-L.Up to 5 variables can be specified in

varlist.

Option

format(%fmt)specifies the format to be used to display the estimated inequality indices. The default is to use a%6.5fformat.

delta()specifies the distributional sensitivity parameters used in computing the relative S-Gini.

epsilon()specifies the inequality aversion parameters used in computing Atkinson inequality index.

alpha()specifies the sensitivity alpha used on the generalised entropy measure.

allrequests that all possible measures are computed and reported. By default, no measure is produced. The Gini and Theil are the deafult measures.

benchmarkcalculates the Relative Poverty Line (Hoffmann, 2001) or Benchmark Income Level (Lambert and Lanza, 2006) for the Gini, Theil-L and Theil-T.The following options specify the measures to be computed and reported.

rmdcontain the "relative mean deviation"covcontain the "coefficient of variation"sdlcontain the "standard deviation of logs"mehrancontain the "Mehran index"pieschcontain the "Piesch index"kakwanicontain the "Kakwani index"mldcontain the "Mean Log Deviation (or generalised entropy measure with sensitivity parameter 0)"ge_1contain the "Generalised entropy measure with sensitivity parameter -1"ge2contain the "Generalised entropy measure with sensitivity parameter 2"

Saved Results

ainequalreturns results in r() format. [Important notice: When multiple variables are entered invarlist, returned results are for all inequality measures of the variable listed.]

AuthorJoao Pedro Azevedo jazevedo@ipea.gov.br IPEA

This is a modified version of the ado inequal7 written by Philippe Van Kerm.

ReferenceAmiel, Y. and Cowell, F.A. (1999) Thinking about Inequality. Cambridge University Press. United Kingdom.

Coulter Ph. (1989), Measuring Inequality -A Methodological Handbook-, Westview Press USA.

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

Hoffmann, R. (2001) Effect of the rise of a person's income on inequality. Brazlian Review of Econometrics v.21, no.2, pp.237-262.

Lambert, P.J. and Lanza, G. (2006) The effect on inequalities of changing one or two incomes. The Journal of Economic Inequality. 4:253-277.

Also seeManual:

[R] lorenzSTB:sg30 (STB-23)On-line: help for inequal (if installed), inequal7 (if installed), ineqdeco (if installed)