hhi: Herfindahl-Hirschman Index In antitrust: Tools for Antitrust Practitioners

Description

Calculate the Herfindahl-Hirschman Index with arbitrary ownership and control.

Usage

 ```1 2 3``` ```HHI(shares, owner=diag(length(shares)), control) ```

Arguments

Let k denote the number of products produced by the merging parties.

 `shares` A length-k vector of product quantity shares. `owner` EITHER a vector of length k whose values indicate which of the merging parties produced a product OR a k x k matrix of ownership shares. Default is a diagonal matrix, which assumes that each product is owned by a separate firm. `control` EITHER a vector of length k whose values indicate which of the merging parties have the ability to make pricing or output decisions OR a k x k matrix of control shares. Default is a k x k matrix equal to 1 if ‘owner’ > 0 and 0 otherwise.

Details

All ‘shares’ must be between 0 and 1. When ‘owner’ is a matrix, the i,jth element of ‘owner’ should equal the percentage of product j's profits earned by the owner of product i. When ‘owner’ is a vector, `HHI` generates a k x k matrix of whose i,jth element equals 1 if products i and j are commonly owned and 0 otherwise. ‘control’ works in a fashion similar to ‘owner’.

Value

`HHI` returns a number between 0 and 10,000

Author(s)

Charles Taragin [email protected]

References

Salop, Steven and O'Brien, Daniel (2000) “Competitive Effects of Partial Ownership: Financial Interest and Corporate Control” 67 Antitrust L.J. 559, pp. 559-614.

`other-methods` for computing HHI following merger simulation.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```## Consider a market with 5 products labeled 1-5. 1,2 are produced ## by Firm A, 2,3 are produced by Firm B, 3 is produced by Firm C. ## The pre-merger product market shares are shares = c(.15,.2,.25,.35,.05) owner = c("A","A","B","B","C") nprod = length(shares) HHI(shares,owner) ## Suppose that Firm A acquires a 75% ownership stake in product 3, and ## Firm B get a 10% ownership stake in product 1. Assume that neither ## firm cedes control of the product to the other. owner <- diag(nprod) owner[1,2] <- owner[2,1] <- owner[3,4] <- owner[4,3] <- 1 control <- owner owner[1,1] <- owner[2,1] <- .9 owner[3,1] <- owner[4,1] <- .1 owner[1,3] <- owner[2,3] <- .75 owner[3,3] <- owner[4,3] <- .25 HHI(shares,owner,control) ## Suppose now that in addition to the ownership stakes described ## earlier, B receives 30% of the control of product 1 control[1,1] <- control[2,1] <- .7 control[3,1] <- control[4,1] <- .3 HHI(shares,owner,control) ```