Herfindahl-Hirschman Index

Description

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

Usage

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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 charles.taragin@usdoj.gov

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.

See Also

other-methods for computing HHI following merger simulation.

Examples

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## 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)

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