*! version 1.1 18Oct2016
help isograph

Title

isograph -- inequality over logit ranks of social hierarchy

Syntax

isograph yvar [if] [in] [weight][,options]

Description

isograph The Isograph describes inequalities in different income levels,
thus providing the overall pattern of inequality together with level-specific
inequalities, serving as Meta-Gini. The formal definition of Isograph is as follows:
ISO_i=(ln((income_i)/median(income)))/(logit(r_i))
Where logit(r) = ln(r/(1-r)) and r_i is element of ]0,1[ and
is the fractional rank order of income quantiles.
For individual i of income_i, the fractional rank is r_i. The value X_i= logit(r_i),
the "logit rank", varies from minus to plus infinite, with a value of 0 for the median.

Options

repeats(n) Provides bootstrap based confidence intervals (95%) with n iterations.

seed(n) Sets the seed for the bootstrapping.

span(n) sets the span of the logitrank default is from -3 to 3. The span is always symmetrical.
In case where there are not enough observations in the left of right tail of the distribution, the result
for this tail would be null.

Examples

use http://www.louischauvel.org/psid9707.dta , clear

isograph equivalent_income [weight=wgt]
isograph equivalent_income [weight=wgt], repeats (10) seed(3739) span(4)

References

Chauvel, L. (2016). The intensity and shape of inequality: the ABG method of distributional analysis. Review of Income and Wealth, 62(1), 52-68.

Chauvel, L. an Bar-Haim, E. (2016) Varieties of Capitalism (VoC) and Varieties of Distributions (VoD): How Welfare Regimes Affect the Pre- and
Post-Transfer Shapes of Inequalities? LIS working papaer series, No. 677

Author

Louis Chauvel, PEARL Institute for Research on Socio-Economic Inequality (IRSEI), University of Luxembourg, louis.chauvel@uni.lu
Eyal Bar-Haim, PEARL Institute for Research on Socio-Economic Inequality (IRSEI), University of Luxembourg, eyal.bar-haim@uni.lu