Modified Herfindahl–Hirschman (MHHI) Calculation*

[Thomas Fuerher]

Dear all,

I am new to STATA and tried to calculate a measure that captures the ownership concentration within a given industry. I have also posted the equation of the MHHI below. My file contains data from the respective firms and the investors from 2000 to 2019. I am struggling to implement a code that considers all the other investor's ownership if the investor is invested in its competitors too...

• s_j is the market share of firm j
• gamma_ij is the control share of firm j by shareholder i
• beta_ij is the ownership share of firm j
• beta_ik indexes firm j's competitors

Here is an exemplary sample of my database:

• mgrno= unique identification number of the shareholder
• Cusip= unique identification number of the firm
• consownership=ownership share
• instvoting=control share

datemerge	mgrname	mgrno	cusip	consownership	instvoting	marketshare
2016q4	Investor 1	47833	0790X10	10%	10%	30%
2016q4	Investor 2	10177	0790X10	15%	12%	30%
2016q4	Investor 3	11800	0790X10	13%	13%	30%
2016q4	Investor 4	54345	0790X10	12%	10%	30%
2016q4	Investor 1	47833	7089W10	10%	10%	40%
2016q4	Investor 2	10177	7089W10	15%	12%	40%
2016q4	Investor 3	11800	7089W10	13%	13%	40%
2016q4	Investor 4	54345	7089W10	12%	12%	40%
2016q4	Investor 1	47833	14744810	10%	10%	30%
2016q4	Investor 2	10177	14744810	15%	15%	30%
2016q4	Investor 3	11800	14744810	13%	10%	30%
2016q4	Investor 4	54345	14744810	12%	10%	30%

I would be grateful for any help on this, and I hope fellow researchers consider this a useful post!

Thank you,
Thomas