{smcl} {hline} help for {hi:richness} {hline} {title:Command to compute measures of (income) richness as defined by Peichl, Schaefer and Scheicher (2008)} {p 5 5}Basic syntax: {p 8 14 2} {cmdab:richness} {it:varlist} [{cmd:if} {it:exp}] [{cmd:in} {it:range}] [{it:weight}{cmd: = }{it:exp}] [{cmd:,} {cmdab:rl:ine(}{it:rl}{cmd:)} | {cmdab:rv:al(}{it:rv}{cmd:)} {cmdab:rn:umber(}{it:rn}{cmd:)} {cmdab:rlf:ix}] {break}{break} {p 8 8 2} {cmd:aweights} and {cmd:fweights} are allowed; see help {help weights:weights}. {title:Description:} {p 1 5 2} {cmd:richness} computes the following richness measures based on the (income) distribution for each {it:varname} of {it:varlist}: {p 5 5 2} - {it:headcount ratio}: fraction of people above the richness line, {p 5 5 2} - {it:FGTT1(a)}: a series of concave (T1 axiom) FGT richness indices with parameters alpha = 0.1, 0.3 and 1. {p 5 5 2} - {it:Cha(b)}: a series of concave (T1 axiom) Chakravaty richness indices with parameters beta = 0.1, 0.3, 1, 3and 10. {p 5 5 2} - {it:FGTT2(a)}: a series of convex (T2 axiom) FGT richness indices with parameters alpha = 1 and 2. {p 5 5 2} - {it:RMed}: absolute Medeiros (2006) richness index. {p 1 5 2} The richness line is either directly specified by the user or computed relative to the median or mean of {it:varname}, see under "options" below. {p 1 5 2} For the calculation of income richness, the income may not be negative. Therefore, cases with {it:varname} less than zero are omitted in the calculation, whereas values of zero are used for the calculation. {title:Options:} {p 1 5 2} There are two ways of defining the richness line: {p 5 5 2} {cmd:rline(}{it:rl}{cmd:)} manually defines a number {it:rl} as the (absolute) richness line (can be any positive number, macro or scalar). {break} If {cmd:rline} is not used, the richness line is computed relatively (see below). {p 5 5 2} The relative calculation of the richness line is based on a multiplier of a parameter of the distribution of {it:varname}. {break} {cmd:rnumber(}{it:rn}{cmd:)} defines the multiplier {it: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%). {break} {cmd:rval(}{it:rv}{cmd:)} defines the distributional parameter {it:rv}, which can be either {cmd:median} (default) or {cmd:mean}. {break} {cmd:rlfix} specifies that the richness line of the first {it:variable} of {it:varlist} is fixed and used for all other {it:variables} of {it:varlist}. {p 1 1 2} If none of the options is specified, a default richness line of 200% of the median is assumed.{break} If both ways (absolute and relative) are specified, the (absolute) richness line defined by {cmd:rline} is used. {title:The output and saved results} {p 1 5 2} {cmd:richness} displays a matrix of the computed results and stores the following results in {cmd:r()}: {p 5 8 2} {it:RR_{it:varname}} is the matrix with the stored results for {it:varlist}, {p 5 8 2} {it:Rline_{it:varname}} is the value of the (computed or specified) richness line for {it:varname}, {p 5 8 2} {it:R_HCR_{it:varname}} is the headcount index (as a decimal) for {it:varname}, {p 5 8 2} {it:R_FGTT1_x_{it:varname}} is the concave FGT (T1 axiom) index with alpha = 0.1(x=10), 0.3(x=30) and 1(x=100) for {it:varname}, {p 5 8 2} {it:R_Cha_x_{it: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 {it:varname}, {p 5 8 2} {it:R_FGTT2_alpha_{it:varname}} is the convex FGT (T2 axiom) index with alpha = 1 or 2 for {it:varname}. {p 5 8 2} {it:R_Med_{it:varname}} is the absolute Medeiros index for {it:varname}. {title:Examples} {cmd} 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 {text} {title:Acknowledgements} {p 1 5 2}Thanks to Stephen Jenkins and Joe Newton for useful suggestions and feedback. {title:References} {p 1 5 2}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. {p 1 5 2}Peichl, Andreas, Schaefer, Thilo and Scheicher, Christoph (2008): Measuring Richness and Poverty - A micro data application to Europe and Germany, IZA discussion paper 3790. {title:Author} Andreas Peichl IZA Institute for the Study of Labor, Bonn, Germany peichl@iza.org www.iza.org {title: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