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Re: st: RE: Computing Herfindahl-Hirschman index


From   Syed Basher <syed.basher@yahoo.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Computing Herfindahl-Hirschman index
Date   Fri, 10 Dec 2010 11:52:06 -0800 (PST)

Dear Nick,

Sorry about the delay to thank your assistance. I am glad to know other variations of the HH index, and the helpful -ineq- routine. Thank you very much.

Syed Basher
Qatar National Food Security Program

--- On Wed, 12/8/10, Nick Cox <n.j.cox@durham.ac.uk> wrote:

> From: Nick Cox <n.j.cox@durham.ac.uk>
> Subject: st: RE: Computing Herfindahl-Hirschman index
> To: "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
> Date: Wednesday, December 8, 2010, 3:20 PM
> The (minor) bad news is that the data
> structure here is not helpful for this purpose, as Antoine
> Terracol implies in his reply, although the -reshape- is one
> line. 
> 
> The good news is that this beast has often been programmed,
> often under a different name. It, or its complement in 1, is
> also known (e.g.) as Simpson's index, especially in ecology,
> as heterozygosity and as one of several things called the
> Gini index. Invoking the name Herfindahl gets nods in
> economics, but he was not the first discoverer. (Hirschman
> as I recall proposed not this formula, but something else.)
> 
> 
> Using e.g. -ineq- from SSC I imagine code like this: 
> 
> reshape long item, i(importer) 
> ineq item, by(importer) gensim(herfindahl) 
> 
> You can -reshape- back if desired. 
> 
> Nick 
> n.j.cox@durham.ac.uk
> 
> 
> Syed Basher
> 
> I have the following (hypothetical) trade dataset which
> contains imported items by importer.
> 
> importer  | item1 item2..... item20
> -----------------------------------
> 11        |  10      20        80 
> 12        |   5       7         9 
> 13        |           1        
> 14        |  
> 2                 6
> ...       |
> 20        |   8       9
> 
> I would like to obtain the following table/data: 
> 
> importer  | item1      item2   .... item20
> -------------------------------------------
> 11        |  1600     2921.84      
> 7091.41 
> 12        |   400      357.92
>         89.75
> 13        |             
> 7.30        
> 14        |    64
>                     39.88
> ...       |
> 20        |  1024      591.67
> 
> 
> where, say, the value 1600 is obtained using the formula
> (si*100)^2, where si is the share of importer11 in item1 and
> is obtained using 10/25,   25 is the sum of all entries in
> item1. This will allow me to get the 
> Herfindahl-Hirschman index by importer for each item.
> 
> 
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