help for bipolarA. Fusco, P. Van Kerm (May 2020, May 2011)

Title

bipolar -- Measures of (Income) Bi-polarization

Syntax

bipolar
varname
[weight]
[if exp]
[in range]
[, options]

rankcut(#) specifies a cut-off rank to split population into high and low income groups; default is 0.5

levelcut(#) specifies a cut-off income level to split population into high and low income groups

posonly restricts estimation to positive values of varname

format(%fmt) display format; default is format(%4.3f)

varlist may contain time-series operators; see tsvarlist.

bootstrap, jackknife, svy bootstrap, and svy jackknife prefixes are allowed; see prefix.

fweight, aweight and pweight are allowed; see help weights.

Description

bipolar calculates measures of income bi-polarization.

bipolar takes a numeric variable as input (typically data on income)
and reports the bi-polarization measures suggested by Foster and Wolfson (1992,2010),
Zhang and Kanbur (2001), and Deutsch et al. (2007).

Bi-polarization measures attempt to capture how much a random variable is concentrated around two `poles' (high and low (income) groups):
bi-polarization measures increase with the concentration of observations within the two poles/groups and
with the separation between the poles/groups.
Bi-polarization measures require the groups to be determined a priori, typically (but not necessarily) as above vs. below the median---leading to two equally-sized groups.
See section 4.4 of the sgini online manual
for details about formulas of the indices calculated by bipolar. More generally, see Nissanov et al (2010) and Duclos and Taptue (2014) for surveys on measures
of income (bi-)polarization.

bipolar does not provide sampling variance estimates (as an r-class command) but it is easily bootstrapped using
a bootstrap or prefix.

Options

rankcut(#) specifies a cut-off rank (0<#<1) to split population into high and low income groups. Measures
of bi-polarization typically consider a population split in two equal-sized groups, that is
use a rank of 0.5. This is the default for bipolar. An alternative rank for splitting
the population into unequal-sized groups can be specified with rankcut(#).
The Foster Wolfson index becomes however undefined in this case.

levelcut(#)} specifies a cut-off income level to split population into high and low income groups
as an alternative to specify an income rank. Choosing an income cut-off typically leads to unequal-sized groups
(unless the median is specified and there is no tied observations at the median).
The Foster Wolfson index is then undefined. rankcut(#) and levelcut(#) are mutually exclusive.

posonly restricts estimation to positive values for varname. By default,
all data are included in computations: bipolar will not discard observations with
negative or zero income.

format(%fmt) controls the display format; default is format(%4.3f).

Saved Results

Scalars

r(N) number of observations

r(sum_w) sum of weights

r(share_low) sample proportion in low income group

r(cutpoint) value splitting low and high income groups

r(Gini) overall Gini index

r(GB) 'Between Group' Gini

r(GW) 'Within Group' Gini

r(ZK) Zhang and Kanbur (2001) index

r(FW) Foster and Wolfson (1992, 2010) index

r(DHS) Deutsch Hanoka Silber (2007) index

Macros

r(varname) varlist

Dependencies

bipolar requires sgini available on the Statistical Software Components (SSC) archive
(ssc describe sgini).

Examples

. use http://www.stata-press.com/data/r9/nlswork , clear

. gen w = exp(ln_wage)

. bipolar w if year==88

. bipolar w if year==88 , rankcut(0.90)

. bootstrap FW=r(FW), reps(50): bipolar w if year==88 & !mi(w)

. jackknife FW=r(FW) : bipolar w if year==88 & !mi(w)

References

Deutsch, J., M. Hanoka & J. Silber (2007), On the Link between the Concepts of Kurtosis and Bipolarization, Economics Bulletin, 4(36): 1-6.

Duclos J.-Y., Taptue, A.-M. (2014), Polarization, in Atkinson, A.B. & F. Bourguignon (eds). Handbook of Income Distribution (vol 2A), chapter 5, North Holland.

Foster, J. E. & M. C. Wolfson (1992), Polarization and the Decline of the Middle Class: Canada and the U.S., mimeo.

Foster, J. E. & M. C. Wolfson (2010), Polarization and the Decline of the Middle Class: Canada and the U.S., Journal of Economic Inequality 8(2): 247-273.

Nissanov Z., A. Poggi & J. Silber (2010), Measuring bi-polarization and polarization: a survey, in Deutsch J. & J. Silber (eds). The Measurement of Individual Well-Being and group Inequalities. Essays in memory of Z.M. Berrebi, chapter 3.

Zhang, X. & R. Kanbur (2001), What Difference Do Polarization Measures Make? An Application to China, Journal of Development Studies 37(3): 85-98.

Also see

Online: sgini (if installed), anogi (if installed) among several others

Authors

Alessio Fusco, Luxembourg Institute of Socio-Economic Research, alessio.fusco@liser.lu

Philippe Van Kerm, Luxembourg Institute of Socio-Economic Research and University of Luxembourg, philippe.vankerm@liser.lu

Acknowledgments

This work was part of the MeDIM and WealthPort projects
supported by the Luxembourg Fonds National de la Recherche (contracts FNR/06/15/08 and C09/LM/04)
and by core funding for CEPS/INSTEAD by the
Ministry of Higher Education and Research of Luxembourg.