# Herfindahl-Hirschman Index Calculate the Herfindahl-Hirschman Index with arbitrary ownership and control. Let k denote the number of products produced by the merging parties below. ```r HHI(shares, owner = diag(length(shares)), control) ``` ## Arguments - `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. ## Returns `HHI` returns a number between 0 and 10,000 ## 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 . ## Examples ```r ## 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) ``` ## References Salop, Steven and O'Brien, Daniel (2000) Competitive Effects of Partial Ownership: Financial Interest andCorporate Control 67 Antitrust L.J. 559, pp. 559-614. ## See Also `HHI-Methods` for computing HHI following merger simulation. ## Author(s) Charles Taragin ctaragin+antitrustr@gmail.com

HHI-Functions function