help isoginiL. Chauvel (March 2024)

Title

isogini -- Stata module to estimate isogini measures at different percentiles plus sigma and pi (version 1.0.2 )

Syntax

isogini varname [if] [in] [weight]
[, options]

rep(numlist) bootstrap repeats; REP(n)

Description

isogini produces estimates of isogini inequality measures at percentiles 10 25 50 75 and 90.

Rapid bootstrap n>20 is provided to generate the standard errors of estimates.

See, among many others, Chauvel (2016 & 2024).

Many thanks to Philippe Van Kerm for a precise review of the earlier version of this ssc install isogini module.

Option

Option concerns the number n of bootstrap iterations.

Selection of indices

rep(numlist) n > 20 the number of iterations; if n <= 20 or no option: no bootstrap is processed (sd=0) .

Example 1: isogini of a Gibrat distribution

clear

set obs 20000

gen income=exp(rnormal())

isogini income

ret li

isogini income , rep(30)

ret li

Example 2: 3 DLL distributions with gini=0.30 but very different poverty rates

Example 2: see “dissymmetric log-logit” DLL distribution Chauvel 2023:18

clear

set obs 100000

gen p=(_n-.5)/_N

gen inc1=(p/(1-p))^.3

gen inc2=(p^(.20)/(1-p)^(.353))

gen inc3=(p^(.365)/(1-p)^(.265))

capt ssc install fastgini

isogini inc1, rep(30)

ret li

fastgini inc1

isogini inc2, rep(30)

ret li

fastgini inc2

isogini inc3, rep(30)

ret li

fastgini inc3

Stored results

isogini stores the following in r().

The indices and their standard deviations "sd" are saved in scalars.

Scalars

r(ig10) => isogini at first decile threshold d1

r(sdig10) => ig10 standard deviation

r(ig50) => isogini at the median = p50 percentile threshold

r(sdig50) => ig50 standard deviation

r(ig25) => etc.

r(sigma) => sigma coefficient etc.

r(ssigma) => its standard deviation

r(pi) => pi coefficient etc.

r(spi) => its standard deviation

References

Chauvel, L. (2016), The Intensity and Shape of Inequality: The ABG Method of Distributional Analysis.
Review of Income and Wealth, 62: 52-68. https://doi.org/10.1111/roiw.12161 https://www.roiw.org/2016/n1/3.pdf

Chauvel, L. & E. Bar-Haim (2016), "ISOGRAPH: Stata module to compute inequality over logit ranks of social hierarchy," Statistical Software Components S458255, Boston College Department of Economics, revised 08 Jun 2017.

Chauvel, L. (2023), "Isograph and LaSiPiKa Distribution: The Comparative Morphology of Income Inequalities and Intelligible Parameters of 53 LIS Countries 1967-2020," LIS WP 852. https://www.lisdatacenter.org/wps/liswps/852.pdf

Chauvel, L. (2024), Isogini as a set of indicators to compare trends and shapes of income inequality: The fading Swedish middle class society in a world of diverse dynamics. https://www.lisdatacenter.org/newsletter

Author

Louis Chauvel, University of Luxembourg, louis.chauvel@uni.lu

Citation

Chauvel, L. (2024). isogini - Stata module to estimate isogini measures at different percentiles ,
Statistical Software Components S459299, Boston College Department of Economics. Available from
http://ideas.repec.org/c/boc/bocode/s459299.html.

Also see

User-written command:
isograph