Monday, February 4, 2013

Concentration Ratios: The Case of Anheuser Busch and Modelo

On Friday, the Wall Street Journal reported that

U.S. Sues to Block $20 Billion Beer Merger
WSJ Feb 1, 2013

Picture by WSJ 

When the government thinks of opposing a merger like this, they try to discern whether an industry is overly concentrated, and thus prone to monopoly like behavior; they often use two ratios.  The first is the 4-firm concentration ratio, simply the sum of the four largest producers.  The second ratio is the Herfindahl-Hershman index, the sum of the squared market values of all firms in the industry.  The range of values for this index are close to zero for a highly populated, highly competitive industry (say 100 firms, each with 1% market share)  to a maximum of 10,000 for a case where one firm has 100% of the market.

The Department of Justice website gives more details on the HH index, noting that values in excess of 2500 are considered to have excess concentration.

So what is the HH index for the beer industry and what are the problems with the use of this method?

For the distribution of market shares noted above, the HH index would be equal 2766 before the merger and 3312 after.  The calculations are shown below.

Company Market Share Market Sh Squared Mkt Sh with merger Mkt. sh with merger sq
Ann Busch 39 1521
Modelo 7 49 46 2116
MillerCoors 26 676 26 676
Heineken 6 36 6 36
Others 22 484 22 484
Sum 100 2766 100 3312

This HH can be  a very useful ratio.  But I want to illustrate some of its problems.  First, note that when we square values, higher numbers produce more extreme values.  Note that the squares associated with, say 1, 2, 3, and 5 produce ever increasing square values of 1, 4, 9 and 25.  Larger market shares produce larger numbers.

So here is a first limitation to note:  I took all the 'other' beer distributors and grouped them in one category, resulting in a 22% market share.  That is, I artificially created a company with a 22% market share.  What is the impact of this?  Well, let's change that assumption.  Let's now assume there are 11 'other' competitors, each with a 2% market share.

Company Market Share Market Sh Squared Mkt Sh with merger Mkt. sh with merger sq
Ann Busch 39 1521
Modelo 7 49 46 2116
MillerCoors 26 676 26 676
Heineken 6 36 6 36
Others           a 2 4 2 4
b 2 4 2 4
c 2 4 2 4
d 2 4 2 4
e 2 4 2 4
f 2 4 2 4
g 2 4 2 4
h 2 4 2 4
i 2 4 2 4
j 2 4 2 4
k 2 4 2 4
Sum 100 2326 100 2872

The HH index is substantially lower, although the merger is still above the limit of 2500 set by the DOJ.

A second and more fundamental criticism of the HH index concerns the definition of 'market'.  Some natural questions arise.  What is the market?

OK, let's start with geography to define our market.  Is is just International? Domestic?  Within a state?  I'll bet more Red Hook is sold in Seattle than in Philly.  Does that make Red Hook anti-competitive in Seattle?

Perhaps more fundamental, what is a market in terms of the product?  Think of Powerade, a low or zero calorie flavored drink.  What comprises its market?  Flavored drinks?  Bottled water?  Soft Drinks?  Beer?  Okay, I'll give you that one - but other questions have less obvious answers.  Does the market for beer include wine?  How about wine spritzers, etc?

And --- if we turn to technology the answers are even more uncertain.  What is the competitive market for HP calculators?  All calculators?  All calculators and personal computers?  Hand-held personal computers?  Cell phones?  Watches with calculators?   Something not yet invented?

The point is - the HH is a useful measure - once we can agree on the market.  But defining that market sometimes requires heroic assumptions.  Think I'll open my Sierra Nevada and contemplate this some more.


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