help for ainequal                                            Joao Pedro Azevedo

Measures of inequality (revised)

ainequal varlist [weight] [if exp] [in range] [, format(%fmt) ATKinson EPSilon(#[ #[ ...]]) RELSGini Delta(#[ #[ ...]]) shorrocks alpha(#[ #[ ...]]) nogini notheil rmd cov sdl mehran piesch kakwani mld ge_1 ge2 all benchmark]

aweights and fweights are allowed; see help weights.


ainequal computes a series of inequality measures of the variables in varlist. It is a revised and upgraded version of inequal7 and inequal published 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 ainequal also 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.


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

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.

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

benchmark calculates 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.

rmd contain the "relative mean deviation" cov contain the "coefficient of variation" sdl contain the "standard deviation of logs" mehran contain the "Mehran index" piesch contain the "Piesch index" kakwani contain the "Kakwani index" mld contain the "Mean Log Deviation (or generalised entropy measure with sensitivity parameter 0)" ge_1 contain the "Generalised entropy measure with sensitivity parameter -1" ge2 contain the "Generalised entropy measure with sensitivity parameter 2"

Saved Results

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


Joao Pedro Azevedo jazevedo@ipea.gov.br IPEA

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


Amiel, 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 see

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