{smcl} {* Help file update 2020-05-03,2011-05-13}{...} {hline} help for {hi:bipolar}{right:A. Fusco, P. Van Kerm (May 2020, May 2011)} {hline} {title:Title} {pstd}{hi:bipolar} {hline 2} Measures of (Income) Bi-polarization {title:Syntax} {p 8 15 2} {cmd:bipolar} {it:varname} [{it:weight}] [{cmd:if} {it:exp}] [{cmd:in} {it:range}] [{cmd:,} {it:options}] {synoptset 22 tabbed} {synopthdr} {synoptline} {synopt :{opt r:ankcut(#)}}specifies a cut-off rank to split population into high and low income groups; default is 0.5{p_end} {synopt :{opt l:evelcut(#)}}specifies a cut-off income level to split population into high and low income groups{p_end} {synopt :{opt pos:only}}restricts estimation to positive values of {it:varname}{p_end} {synopt :{opth for:mat(%fmt)}}display format; default is {cmd:format(%4.3f)}{p_end} {synoptline} {p 4 8 2} {it:varlist} may contain time-series operators; see {help tsvarlist}. {p_end} {p 4 6 2}{cmd:bootstrap}, {cmd:jackknife}, {cmd:svy bootstrap}, and {cmd:svy jackknife} prefixes are allowed; see {help prefix}.{p_end} {p 4 6 2}{cmd:fweight}, {cmd:aweight} and {cmd:pweight} are allowed; see help {help weights:weights}. {p_end} {title:Description} {pstd} {hi:bipolar} calculates measures of income bi-polarization. {p_end} {pstd} {hi: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). {p_end} {pstd} 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 {hi:sgini} {browse "http://www.vankerm.net/stata/manuals/sgini.pdf":online manual} for details about formulas of the indices calculated by {cmd:bipolar}. More generally, see Nissanov et al (2010) and Duclos and Taptue (2014) for surveys on measures of income (bi-)polarization. {p_end} {pstd} {cmd:bipolar} does not provide sampling variance estimates (as an r-class command) but it is easily bootstrapped using a {cmd:bootstrap} or {svy bootstrap} prefix. {p_end} {title:Options} {phang} {opt r:ankcut(#)} 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 {hi:bipolar}. An alternative rank for splitting the population into unequal-sized groups can be specified with {opt r:ankcut(#)}. The Foster Wolfson index becomes however undefined in this case. {p_end} {phang} {opt l:evelcut(#)}} 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. {opt r:ankcut(#)} and {opt l:evelcut(#)} are mutually exclusive. {p_end} {phang} {opt pos:only} restricts estimation to positive values for {it:varname}. By default, all data are included in computations: {hi:bipolar} will not discard observations with negative or zero income. {p_end} {phang} {opth format(%fmt)} controls the display format; default is {cmd:format(%4.3f)}. {p_end} {title:Saved Results} {synoptset 15 tabbed}{...} {p2col 5 15 19 2: Scalars}{p_end} {synopt:{cmd:r(N)}}number of observations{p_end} {synopt:{cmd:r(sum_w)}}sum of weights{p_end} {synopt:{cmd:r(share_low)}}sample proportion in low income group{p_end} {synopt:{cmd:r(cutpoint)}}value splitting low and high income groups{p_end} {synopt:{cmd:r(Gini)}}overall Gini index{p_end} {synopt:{cmd:r(GB)}}'Between Group' Gini{p_end} {synopt:{cmd:r(GW)}}'Within Group' Gini{p_end} {synopt:{cmd:r(ZK)}}Zhang and Kanbur (2001) index{p_end} {synopt:{cmd:r(FW)}}Foster and Wolfson (1992, 2010) index{p_end} {synopt:{cmd:r(DHS)}}Deutsch Hanoka Silber (2007) index{p_end} {synoptset 15 tabbed}{...} {p2col 5 15 19 2: Macros}{p_end} {synopt:{cmd:r(varname)}}{it:varlist}{p_end} {title:Dependencies} {pstd} {hi:bipolar} requires {hi:sgini} available on the Statistical Software Components (SSC) archive ({net "describe sgini, from(http://fmwww.bc.edu/repec/bocode/s/)":ssc describe sgini}). {p_end} {title:Examples} {p 8 12 2}{inp:. use http://www.stata-press.com/data/r9/nlswork , clear } {p 8 12 2}{inp:. gen w = exp(ln_wage) } {p 8 12 2}{inp:. bipolar w if year==88} {p 8 12 2}{inp:. bipolar w if year==88 , rankcut(0.90) } {p 8 12 2}{inp:. bootstrap FW=r(FW), reps(50): bipolar w if year==88 & !mi(w)} {p 8 12 2}{inp:. jackknife FW=r(FW) : bipolar w if year==88 & !mi(w) } {title:References} {p 4 8 2}Deutsch, J., M. Hanoka & J. Silber (2007), On the Link between the Concepts of Kurtosis and Bipolarization, Economics Bulletin, 4(36): 1{c -}6. {p 4 8 2}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. {p 4 8 2}Foster, J. E. & M. C. Wolfson (1992), Polarization and the Decline of the Middle Class: Canada and the U.S., mimeo. {p 4 8 2}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{c -}273. {p 4 8 2}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. {p 4 8 2}Zhang, X. & R. Kanbur (2001), What Difference Do Polarization Measures Make? An Application to China, Journal of Development Studies 37(3): 85{c -}98. {title:Also see} {psee} Online: {helpb sgini} (if installed), {helpb anogi} (if installed) among {stata "findit polarization":several others} {title:Authors} {pstd}Alessio Fusco, Luxembourg Institute of Socio-Economic Research, alessio.fusco@liser.lu {pstd}Philippe Van Kerm, Luxembourg Institute of Socio-Economic Research and University of Luxembourg, philippe.vankerm@liser.lu {title:Acknowledgments} {pstd} 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. {* Version 2.0 2020-05-03, 1.0 2011-05-13}