Herfindahl index
Encyclopedia
The Herfindahl index is a measure of the size of firm
s 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 share
s 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
, 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.
The measure is essentially equivalent to the Simpson diversity index used in ecology.
We will 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:
This behavior 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., 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. 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).
where
is the market share of firm 
in the market, and 
is the number of firms. Thus, in a market with two firms that each have 50 percent market share, the Herfindahl index equals 
.
The Herfindahl Index (
) ranges from 
to one, where 
is the number of firms in the market. Equivalently, if percents are used as whole numbers, as in 
instead of 
, the index can range up to 
, or 
.
A HHI index below 0.01 (or 100) indicates a highly competitive index.
A HHI index below 0.15 (or 1,500) indicates an unconcentrated 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 http://www.justice.gov/atr/public/guidelines/hmg-2010.html.
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, 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:
where again, N is the number of firms in the market, and H is the usual Herfindahl Index, as above.
The United States Federal anti-trust authorities 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 Division of the Department of Justice
considers 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.
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).
Corporation
A corporation is created under the laws of a state as a separate legal entity that has privileges and liabilities that are distinct from those of its members. There are many different forms of corporations, most of which are used to conduct business. Early corporations were established by charter...
s in relation to the industry
Industry
Industry refers to the production of an economic good or service within an economy.-Industrial sectors:There are four key industrial economic sectors: the primary sector, largely raw material extraction industries such as mining and farming; the secondary sector, involving refining, construction,...
and an indicator of the amount of competition among them. Named after economists Orris C. Herfindahl and Albert O. Hirschman
Albert O. Hirschman
Albert Otto Hirschman is an influential economist who has authored several books on political economy and political ideology. His first major contribution was in the area of development economics. Here he emphasized the need for unbalanced growth...
, it is an economic
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...
concept widely applied in competition law
Competition law
Competition law, known in the United States as antitrust law, is law that promotes or maintains market competition by regulating anti-competitive conduct by companies....
, antitrust
Antitrust
The United States antitrust law is a body of laws that prohibits anti-competitive behavior and unfair business practices. Antitrust laws are intended to encourage competition in the marketplace. These competition laws make illegal certain practices deemed to hurt businesses or consumers or both,...
and also technology management. It is defined as the sum of the squares of the market share
Market share
Market share is the percentage of a market accounted for by a specific entity. In a survey of nearly 200 senior marketing managers, 67 percent responded that they found the "dollar market share" metric very useful, while 61% found "unit market share" very useful.Marketers need to be able to...
s 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
Monopoly
A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity...
producer. Increases in the Herfindahl index generally indicate a decrease in competition and an increase of market power
Market power
In economics, market power is the ability of a firm to alter the market price of a good or service. In perfectly competitive markets, market participants have no market power. A firm with market power can raise prices without losing its customers to competitors...
, whereas decreases indicate the opposite.
The major benefit of the Herfindahl index in relationship to such measures as the concentration ratio
Concentration ratio
In economics, a concentration ratio is a measure of the total output produced in an industry by a given number of firms in the industry. The most common concentration ratios are the CR4 and the CR8, which means the four and the eight largest firms...
is that it gives more weight to larger firms.
The measure is essentially equivalent to the Simpson diversity index used in ecology.
Example
For instance, 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 will 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
Monopoly
A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity...
. 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 behavior 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., 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. 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).
Formula
where
is the market share of firm in the market, and is the number of firms. Thus, in a market with two firms that each have 50 percent market share, the Herfindahl index equals .The Herfindahl Index (
) ranges from to one, where is the number of firms in the market. Equivalently, if percents are used as whole numbers, as in instead of , the index can range up to , or .A HHI index below 0.01 (or 100) indicates a highly competitive index.
A HHI index below 0.15 (or 1,500) indicates an unconcentrated 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 http://www.justice.gov/atr/public/guidelines/hmg-2010.html.
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, 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:
where again, N is the number of firms in the market, and H is the usual Herfindahl Index, as above.
Problems
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.
The United States Federal anti-trust authorities 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 Division of the Department of Justice
United States Department of Justice Antitrust Division
The United States Department of Justice Antitrust Division is responsible for enforcing the antitrust laws of the United States. It shares jurisdiction over civil antitrust cases with the Federal Trade Commission and often works jointly with the FTC to provide regulatory guidance to businesses...
considers Herfindahl indices between 0.1000 and 0.1800 to be moderately concentrated and indices above 0.2500 to be concentrated. As the market concentration
Market concentration
In economics, market concentration is a function of the number of firms and their respective shares of the total production in a market...
increases, competition
Competition
Competition is a contest between individuals, groups, animals, etc. for territory, a niche, or a location of resources. It arises whenever two and only two strive for a goal which cannot be shared. Competition occurs naturally between living organisms which co-exist in the same environment. For...
and efficiency
Efficiency (economics)
In economics, the term economic efficiency refers to the use of resources so as to maximize the production of goods and services. An economic system is said to be more efficient than another if it can provide more goods and services for society without using more resources...
decrease and the chances of collusion
Collusion
Collusion is an agreement between two or more persons, sometimes illegal and therefore secretive, to limit open competition by deceiving, misleading, or defrauding others of their legal rights, or to obtain an objective forbidden by law typically by defrauding or gaining an unfair advantage...
and monopoly
Monopoly
A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity...
increase.
Intuition
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
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 varianceVariance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
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).See also
- Diversity indexDiversity indexA diversity index is a statistic which is intended to measure the local members of a set consisting of various types of objects. Diversity indices can be used in many fields of study to assess the diversity of any population in which each member belongs to a unique group, type or species...
- Market concentrationMarket concentrationIn economics, market concentration is a function of the number of firms and their respective shares of the total production in a market...
- Market forms
- MicroeconomicsMicroeconomicsMicroeconomics is a branch of economics that studies the behavior of how the individual modern household and firms make decisions to allocate limited resources. Typically, it applies to markets where goods or services are being bought and sold...
- Market dominance strategies
External links
- World Integrated Trade Solution, Calculate Herfindahl-Hirschman Index using UNSD COMTRADE data
- US Department of Justice example and market concentration cutoffs.
- Herfindahl-Hirschman Index Calculator. Web tool for calculating pre- and post-merger Herfindahl index.
- Department of Justice and Federal Trade Commission 2010 Horizontal Merger Guidelines. More detailed information about mergers, market concentration, and competition (from the Department of JusticeUnited States Department of JusticeThe United States Department of Justice , is the United States federal executive department responsible for the enforcement of the law and administration of justice, equivalent to the justice or interior ministries of other countries.The Department is led by the Attorney General, who is nominated...
).