I am trying to calculate the EGI (Ellison and Glaeser's index of geographical concentration) using the STATA module developed by Jay Dev Dubey. I have a query regarding the formula used. The help file on the module states the following:
Ellision and Glaeser's index
EGIi = (GIi - HIi)/(1-HIi)
where, GIi = Sum of squared deivation of ith industry's state employment share from
a measure Ss.
Ss = employment share ith state in the average industry.
Hi = Herfindhal style measure of the plant level concentration of employment in ith
industry.
EGI syntax return and store the Ellision and Glaeser's index for each industry variety
as a new variable. By choosing suitable index option it may also return other components.
Option
However, the 1997 paper has the following formula,

From what I am understanding, the EGI module on STATA is missing the following.

Just wanted to check if my understanding is correct here, or whether the EGI STATA module is correct.
Thanks!
Ellision and Glaeser's index
EGIi = (GIi - HIi)/(1-HIi)
where, GIi = Sum of squared deivation of ith industry's state employment share from
a measure Ss.
Ss = employment share ith state in the average industry.
Hi = Herfindhal style measure of the plant level concentration of employment in ith
industry.
EGI syntax return and store the Ellision and Glaeser's index for each industry variety
as a new variable. By choosing suitable index option it may also return other components.
Option
However, the 1997 paper has the following formula,
From what I am understanding, the EGI module on STATA is missing the following.
Just wanted to check if my understanding is correct here, or whether the EGI STATA module is correct.
Thanks!