Calculating team heterogenity with the Blau-Index

[Claudia Geigenebrger]

Dear all,

currently i am writing my thesis for which i have to perform a data analysis with STATA. I use the STATA version 12.
I examine the top management teams of 50 companies listed in the Forbes500 index over the observation period 2010 until 2016.
First of all i collected data on the highest university degree of the top management team members in the following areas of subject (natural sciences, social sciences, business & economics, law, humanities) per year and per company. These variables on the areas of subjects (humanities, sciences etc.) were counted as dummy variables with 1 if the top management team member has it's highest degree in this area and 0 otherwise.
Then this data was aggregated from a personal level to a company level by calculating the averages for the top management team per year and per company, resulting in the following data:

Here a small excerpt from my data for one company: observationid (combination of companyid and year) companyid (just a random id)

ObeservationID Year Company ID Dummy_Natural Sciences Dummy_Social Sciences Dummy_Business&Economics Dummy_Law Dummy_Humanities

12010 2010 1 0 0 0.8 0 0

12011 2011 1 0 0 0.8 0.15 0

12012 2012 1 0 0 0.8 0.15 0

12013 2013 1 0 0 0.8 0 0

12014 2014 1 0 0 0.6 0 0

12015 2015 1 0 0 0.5 0 0.15

12016 2016 1 0 0 0.7 0 0,2


I have to calculate the hetereogeneity of top management teams concerning educational background using the Blau's index, with the formula
B = (1 - ∑(ρ_i)²)where ρ is the percentage of top management team members having the hightest degree in the ith area of subject.

Do you have any idea, what is the right code to calculate the Blau-Index in that way?

I saw i can use the divcat command but i am not sure what the right code looks like.

It would be very nice and really a great help if somebody can show me the right code.


Thank you very much for your help in advance!


Best regards,
Claudia

[Maarten Buis]

What you called dummies, are not dummies in your data. A dummy or indicator variable is a variable that can take only two values 0 (false) or 1 (true). Instead you have proportions.

Your proportions don't add up to one. Isn't that required for the Blau index? I am not sure, but I would look into that before continuing.

[Phil Bromiley]

To add to Maarten's comment, let's assume your proportions are right. You need to do a few manually to check that the program is doing what you intend. Then

g bi=(1 - phum - plaw - pSocialSciences)^2

Just add the other disciplines to the list. I'm not sure you have the right formula. A lot of such formulas do 1 minus the sum of the squared proportions, not the square of 1 minus the sum of the proportions.

[Nick Cox]

Phil: I think what is needed is more like

g bi = 1 - phum^2 - plaw^2 - pSocialSciences^2