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Re: st: Herfindahl, segregation index


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Herfindahl, segregation index
Date   Wed, 26 Jan 2011 11:38:49 -0500

Tomeka Davis <soctmd@langate.gsu.edu>:
I had a look at -seg- and it does not seem to support weights, and it
does not operate on unit record data, so you would have to -collapse-
or otherwise modify an individual-level dataset (probably using
weights) to prepare it for -seg-. -seg- seems to be designed mostly
for use on US Census tract- or block-level data. If you had
tract-level data with shares already defined as variables, the HHI
would be computed with a single call to -generate- e.g.
. gen hhi=white^2+black^2+other^2
so I assume you don't have that simple situation. Here is an example
that demonstrates the closest parallel of the output of -seg- to HHI:

webuse nhanes2, clear
* pretend data is unweighted
ta race
qui levelsof race, loc(vs)
qui foreach v of loc vs {
 egen sh`v'=mean(race==`v'), by(region smsa)
 replace sh`v'=sh`v'^2
 la var sh`v' "sq. share race==`v'"
 }
su sh*
egen hhi=rowtotal(sh*)
bys region smsa:g two=(_n>1)
li region smsa sh* hhi if two==0, noo sepby(region)
* stop pretending data is unweighted
egen gp=group(region smsa)
qui levelsof gp, loc(gs)
qui foreach v of loc vs {
 tempvar vi
 g `vi'=race==`v'
 g ws`v'=.
 la var ws`v' "wtd. sq. share race==`v'"
 foreach g of loc gs {
  su `vi' if gp==`g' [aw=finalwgt], mean
  replace ws`v'=r(mean)^2 if gp==`g'
  }
 }
egen whhi=rowtotal(ws*)
li region smsa hhi whhi if two==0, noo sepby(region)
g white=race==1
collapse white black orace hhi whhi ws? sh? [pw=finalwgt], by(region smsa gp)
g norm=(1-whhi)*3/2
qui seg white black orace, by(gp) gen(i indx) p
li region smsa whhi norm indx, noo sepby(region)

Note that if you need to use -seg- on unit-record data, you will first
collapse, then run -seg-, then save under a new name, then go back to
your original data and merge on the output.

On Wed, Jan 26, 2011 at 10:44 AM, Austin Nichols
<austinnichols@gmail.com> wrote:
> Tomeka Davis <soctmd@langate.gsu.edu> :
> If you want the HHI, calculate the sum of squared shares directly,
> perhaps using -egen- or -by- a couple of times, but if you want to use
> the user-written -seg- on SSC you should check out its references,
> particularly the 2002 paper by the same author:
>
> James, David R. and Karl E. Taeuber. 1985. "Measures of segregation."
>      Sociological Methodology 14:1-32
> Massey, Douglas S. and Nancy A. Denton. 1988. "The dimensions of racial
>      segregation." Social Forces 67:281-315.
> Reardon, Sean F., and Glenn Firebaugh. 2002. "Measures of multigroup
>      segregation."  Sociological Methodology 32: 33-67.
> White, Michael J. 1986. "Segregation and diversity measures in population
>      distribution." Population Index 52:198-221.
> Zoloth, Barbara S. 1976. "Alternative measures of school segregation." Land
>      Economics 52:278-298.
>
> On Wed, Jan 26, 2011 at 9:23 AM, Tomeka Davis <soctmd@langate.gsu.edu> wrote:
>> Hello -
>>
>> I would like to compute a racial segregation index for a set of data.  I know -seg- will allow me to do this, but I am not clear on which of the indices computed by -seg- is similar to the Herfindahl.  I would appreciate any advice.
>

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