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Command to compute measures of (income) richness as defined by Peichl, Schaefer> and Scheicher (2008)Basic syntax:

richnessvarlist[ifexp] [inrange] [weight=exp] [,rline(rl)|rval(rv)rnumber(rn)rlfix]

aweightsandfweightsare allowed; see help weights.

Description:

richnesscomputes the following richness measures based on the (income) distribution for eachvarnameofvarlist:-

headcount ratio: fraction of people above the richness line,-

FGTT1(a): a series of concave (T1 axiom) FGT richness indices with parameters alpha = 0.1, 0.3 and 1.-

Cha(b): a series of concave (T1 axiom) Chakravaty richness indices with parameters beta = 0.1, 0.3, 1, 3and 10.-

FGTT2(a): a series of convex (T2 axiom) FGT richness indices with parameters alpha = 1 and 2.-

RMed: absolute Medeiros (2006) richness index.The richness line is either directly specified by the user or computed relative to the median or mean of

varname, see under "options" below.For the calculation of income richness, the income may not be negative. Therefore, cases with

varnameless than zero are omitted in the calculation, whereas values of zero are used for the calculation.

Options:There are two ways of defining the richness line:

rline(rl)manually defines a numberrlas the (absolute) richness line (can be any positive number, macro or scalar). Ifrlineis not used, the richness line is computed relatively (see below).The relative calculation of the richness line is based on a multiplier of a parameter of the distribution of

varname.rnumber(rn)defines the multiplierrn, which can be any positive number and has to be specified in percent but without the "%" symbol (eg. 200, which is the default value, and not "200%" if you want to specify a richness line of 200%).rval(rv)defines the distributional parameterrv, which can be eithermedian(default) ormean.rlfixspecifies that the richness line of the firstvariableofvarlistis fixed and used for all othervariablesofvarlist.If none of the options is specified, a default richness line of 200% of the median is assumed. If both ways (absolute and relative) are specified, the (absolute) richness line defined by

rlineis used.

The output and saved results

richnessdisplays a matrix of the computed results and stores the following results inr():

RR_varnameis the matrix with the stored results forvarlist,

Rline_varnameis the value of the (computed or specified) richness line forvarname,

R_HCR_varnameis the headcount index (as a decimal) forvarname,

R_FGTT1_x_varnameis the concave FGT (T1 axiom) index with alpha = 0.1(x=10), 0.3(x=30) and 1(x=100) forvarname,

R_Cha_x_varnameis the Chakravaty index with beta = 0.1(x=10), 0.3(x=30), 1(x=100), 3(x=300) and 10(x=1000) forvarname,

R_FGTT2_alpha_varnameis the convex FGT (T2 axiom) index with alpha = 1 or 2 forvarname.

R_Med_varnameis the absolute Medeiros index forvarname.

Examples

richness incomerichness income if sex=1 [fw=weight], rline(10000)richness income if sex=1 & region = 2 [fw=weight], rval(mean)richness income if sex=1 & region = 2 [fw=weight], rval(mean) rnumber(300)richness income1 income2, rlfix

AcknowledgementsThanks to Stephen Jenkins and Joe Newton for useful suggestions and feedback.

ReferencesPeichl, Andreas, Schaefer, Thilo and Scheicher, Christoph (2006): Measuring Richness and Poverty - A micro data application to Germany and the EU-15, CPE discussion papers No. 06-11, University of Cologne.

Peichl, Andreas, Schaefer, Thilo and Scheicher, Christoph (2008): Measuring Richness and Poverty - A micro data application to Europe and Germany, IZA discussion paper 3790.

AuthorAndreas Peichl IZA Institute for the Study of Labor, Bonn, Germany peichl@iza.org www.iza.org

Authors previous versionAndreas Peichl & Thilo Schaefer Cologne Center for Public Economics University of Cologne, Germany a.peichl@uni-koeln.de, schaefer@fifo-koeln.de www.cpe-cologne.de

Version 2.0.0 2008-11-18