AHAM
NZENWATA
INTRODUCTION
The Herfindahl index (also known as Herfindahl–Hirschman Index, or HHI)
is a measure of the size of firms in relation to the industry and an indicator
of the amount of competition among them. Named after economists Orris C.
Herfindahl and Albert O. Hirschman, it is an economic concept widely applied in
competition law, antitrust and also technology management. It is defined as the
sum of the squares of the market shares of the 50 largest firms (or summed over
all the firms if there are fewer than 50 within the industry, where the market
shares are expressed as fractions.
The result is proportional
to the average market share, weighted by market share. As such, it can range
from 0 to 1.0, moving from a huge number of very small firms to a single
monopolistic producer. Increases in the Herfindahl index generally indicate a
decrease in competition and an increase of market power of one or few firms,
whereas decreases indicate the opposite. The major benefit of the Herfindahl
index in relationship to such measures as the concentration ratio is that it
gives more weight to larger firms.
APPLICATION OF THE
INDEX
If we take for example, two cases in which the six largest firms produce
90% of the goods in a market:
·
Case 1: All six firms produce 15% each, and
·
Case 2: One firm produces 80% while the
five others produce 2% each.
We assume that the remaining 10% of output is divided among 10 equally
sized producers.
The six-firm concentration ratio would equal 90% for both case 1 and
case 2. But the first case would promote significant competition, where the
second case approaches monopoly. The Herfindahl index for these two situations
makes the lack of competition in the second case strikingly clear:
·
Case 1: Herfindahl index = 6 * 0.152 + 10 *
0.012 = 0.136 (13.6%)
·
Case 2: Herfindahl index = 0.802 + 5 *
0.022 + 10 * 0.012 = 0.643 (64.3%)
This behaviour rests in the fact that the market shares are squared
prior to being summed, giving additional weight to firms with larger size.
The index involves taking the market share of the respective market
competitors, squaring it, and adding them together (e.g. in the market for X,
company A has 30%, B, C, D, E and F have 10% each and G through to Z have 1%
each). If the resulting figure is above a certain threshold then economists
consider the market to have a high concentration (e.g. market X's concentration
is 0.142 or 14.2%). This threshold is considered to be 0.25 in the U.S.,[1]
while the EU prefers to focus on the level of change, for instance that concern
is raised if there is a 0.025 change when the index already shows a
concentration of 0.1.[4] So to take the example, if in market X company B (with
10% market share) suddenly bought out the shares of company C (with 10% also)
then this new market concentration would make the index jump to 0.162. Here it
can be seen that it would not be relevant for merger law in the U.S. (being
under 0.18) or in the EU (because there is not a change over 0.025).
THE HHI MODEL
Where Si = The market share of
firm in the market, and
N = The number of firms.
Thus, in a market
with two firms that each have 50 percent market share, the Herfindahl index (H) is
H
= 0.502 + 0.502 = .50
The Herfindahl
Index (H) ranges from 1/N to one, where N is the number of
firms in the market. Equivalently, if percents are used as whole numbers, as in
75% instead of 0.75, the index can range up to 1002, or 10,000.
Given the above,
·
A HHI index below 0.01 (or 100) indicates a
highly competitive index.
·
A HHI index below 0.15 (or 1,500) indicates
an un-concentrated index.
·
A HHI index between 0.15 to 0.25 (or 1,500
to 2,500) indicates moderate concentration.
·
A HHI index above 0.25 (above 2,500)
indicates high concentration.
A small index indicates a competitive industry with no dominant players.
If all firms have an equal share the reciprocal of the index shows the number
of firms in the industry. When firms have unequal shares, the reciprocal of the
index indicates the "equivalent" number of firms in the industry.
Using case 2 above, we find that the market structure is equivalent to having
1.55521 firms of the same size.
There is also a normalised Herfindahl index. Whereas the Herfindahl
index ranges from 1/N to one, the normalized Herfindahl index ranges from 0 to
1. It is computed as:
H = 
Where again, N is
the number of firms in the market, and H is the usual Herfindahl Index, as
above.
PROBLEMS OF THE
HERFINDAHL INDEX
The usefulness of this statistic to detect and stop harmful monopolies
however is directly dependent on a proper definition of a particular market
(which hinges primarily on the notion of substitutability). For example, if the
statistic were to look at a hypothetical financial services industry as a
whole, and found that it contained 6 main firms with 15% market share apiece,
then the industry would look non-monopolistic. However, one of those firms
handles 90% of the checking and savings accounts and physical branches (and
overcharges for them because of its monopoly), and the others primarily do
commercial banking and investments. In this scenario, people would be suffering
due to a market dominance by one firm; the market is not properly defined
because checking accounts are not substitutable with commercial and investment
banking. The problems of defining a market work the other way as well. To take
another example, one cinema may have 90% of the movie market, but if movie
theatres compete against video stores, pubs and nightclubs then people are less
likely to be suffering due to market dominance.
Another typical problem in defining the market is choosing a geographic
scope. For example, firms may have 20% market share each, but may occupy five
areas of the country in which they are monopoly providers and thus do not
compete against each other. A service provider or manufacturer in one city is
not necessarily substitutable with a service provider or manufacturer in another
city, depending on the importance of being local for the business—for example,
telemarketing services are rather global in scope, while shoe repair services
are local.
Anti-trust authorities in the United States such as the Department of
Justice and the Federal Trade Commission use the Herfindahl index as a
screening tool to determine whether a proposed merger is likely to raise
antitrust concerns [increases of over 0.0100 points generally provoke scrutiny,
although this varies from case to case. The Antitrust authorities consider
Herfindahl indices between 0.1000 and 0.1800 to be moderately concentrated and
indices above 0.2500 to be concentrated. As the market concentration increases,
competition and efficiency decrease and the chances of collusion and monopoly
increase.
When all the firms
in an industry have equal market shares, H = 1/N. The Herfindahl is correlated
with the number of firms in an industry because its lower bound when there are
N firms is 1/N. An industry with 3 firms cannot have a lower Herfindahl than an
industry with 20 firms when firms have equal market shares. But as market
shares of the 20-firm industry diverge from equality the Herfindahl can exceed
that of the equal-market-share 3-firm industry (e.g., if one firm has 81% of
the market and the remaining 19 have 1% each H=0.658). A higher Herfindahl
signifies a less competitive industry.
DECOMPOSITION OF
THE INDEX
If we suppose that
N firms share all the market, then the index can be expressed as:
where N is the number of firms, as above, and V is the statistical
variance of the firm shares, defined as:
If all firms have equal (identical) shares (that is, if the market
structure is completely symmetric, in which case Si = 1/N for all i)
then V is zero and H equals 1/N. If the number of firms in the market is held
constant, then a higher variance due to a higher level of asymmetry between
firms' shares (that is, a higher share dispersion) will result in a higher
index value. See Brown and Warren-Boulton (1988), also see Warren-Boulton
(1990).
REFERENCES
Brown, Donald M.;
Warren-Boulton & Frederick R. (1988). Testing the Structure-Competition
Relationship on Cross-Sectional Firm Data. Discussion paper 88-6. Economic
Analysis Group, U.S. Department of Justice.
Hirschman, Albert
O. (1964). "The Paternity of an Index". The American Economic Review
(American Economic Association) 54 (5): 761. JSTOR 1818582.
Warren-Boulton
& Frederick R. (1990). "Implications of U.S. Experience with
Horizontal Mergers and Takeovers for Canadian Competition Policy". In
Mathewson, G. Franklin et al. (eds.). The Law and Economics of Competition
Policy. Vancouver, B.C.: The Fraser Institute. ISBN 0889751218.
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