help for richness

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

Basic syntax:

richness varlist [if exp] [in range] [weight = exp] [, rline(rl) | rval(rv) rnumber(rn) rlfix]

aweights and fweights are allowed; see help weights.


richness computes the following richness measures based on the (income) distribution for each varname of varlist:

- 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 varname less than zero are omitted in the calculation, whereas values of zero are used for the calculation.


There are two ways of defining the richness line:

rline(rl) manually defines a number rl as the (absolute) richness line (can be any positive number, macro or scalar). If rline is 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 multiplier rn, 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 parameter rv, which can be either median (default) or mean. rlfix specifies that the richness line of the first variable of varlist is fixed and used for all other variables of varlist.

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 rline is used.

The output and saved results

richness displays a matrix of the computed results and stores the following results in r():

RR_varname is the matrix with the stored results for varlist,

Rline_varname is the value of the (computed or specified) richness line for varname,

R_HCR_varname is the headcount index (as a decimal) for varname,

R_FGTT1_x_varname is the concave FGT (T1 axiom) index with alpha = 0.1(x=10), 0.3(x=30) and 1(x=100) for varname,

R_Cha_x_varname is the Chakravaty index with beta = 0.1(x=10), 0.3(x=30), 1(x=100), 3(x=300) and 10(x=1000) for varname,

R_FGTT2_alpha_varname is the convex FGT (T2 axiom) index with alpha = 1 or 2 for varname.

R_Med_varname is the absolute Medeiros index for varname.


richness income richness 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


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


Peichl, 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.


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

Authors previous version

Andreas 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