# Concentration indexes - Four firm concentration ratios, Herfindahl Hershman indexes (HHI)

Four-Firm Concentration Ratio
Concentration ratios and indexes are used to measure a firm’s concentration in an industry at one point in time. The numbers derived from the ratios and indexes assist in gauging the competitive or monopolistic environment in a given industry. One of the most well known concentration ratios is the four-firm concentration ratio. This ratio measures the percentage of sales of the four largest firms in the market divided by the total market sales. The larger the ratio, the less competition there is in the market; the smaller the ratio, the more competitive the market is. More specifically, a ratio of less than 40% is considered competitive; a ratio of more than 40% is considered an oligopoly. The following equation shows how to calculate the ratio:

c4=w1+w2+w3+w4, wi= Si/St

Si is equal to the individual sales of the firm and St is equal to all firm’s sales.

Below is a table with concentration ratios of several industries. This data was retrieved from the 2002 US Economic Census of Manufacturing.

Industry
Automotive Vehicles 87.3
Breakfast Cereal 78.4
Computer & Peripherals 49.8
Fiber Optic Cables 66.9
Industrial Gas 63.8
Plastic Bottles 42.3
Plastic & Rubber Products 7.6
Printing Ink 54
Poultry 46.3
Newspapers- Daily 22.1

Looking to the automotive industry as an example, we see the ratio is 87.3. This means that 87.3% of the industry is controlled by the top four firms. While interpreting the ratios, there are a few things to keep in mind. Bruce Domazlicky discusses two examples of this in his paper “From Theory to Reality: Concentration Ratios”. On the one hand, in some cases if the market is narrowly defined, the ratios can be misleading. Breakfast cereal has a ratio of 78.4%. This is very high. But recall that in the world of breakfast foods, cereal is one of many choices. So although the breakfast cereal market is dominated by a few, the breakfast food market is much broader. Waffles, bagels and breakfast pastries, etc are in direct competition with breakfast cereal, and are important to consider.
On the other hand, some markets are just the opposite, with low concentration ratios. Typically this would indicate a very competitive market. But looking at the market for newspapers, for example, we see that this is not the case. The majority of newspapers are sold in a local market with very little competition. Take Indianapolis for instance. With the exception of a few county newspapers, the Indianapolis Star holds a monopoly on print media in the area. However the industry concentration ratio of 22.1% applies to the four largest national newspapers. This ratio would suggest a competitive market. Obviously, that is not the case.

Herfindahl-Hirschman Index
The Herfindahl-Hirschman Index (HHI) is another valuable tool to use when measuring competitiveness in an industry. It is calculated by taking the sum of the squares of the market shares of all firms in an industry and multiplying by 10,000. The equation is as follows:

HHI = 10,000 ∑wi²

Just as with the concentration ratio, wi= Si/St, Si is the individual firm's sales and St is the industry sales. The value of the index will be between 0 and 10,000. If there were only one firm in the industry, the index would be 10,000 because one firm would have 100% of market share. Lots of firms, each with a small market share, is indicative of competition. One practical application of the HHI is used the Department of Justice. The index is used when assessing mergers. An HHI of less than 1000 signifies an unconcentrated market. An HHI between 1000 and 1800 signifies a moderately concentrated market. An HHI over 1800 is a concentrated market. Anti-trust concerns would be raised by any transaction that would cause the index (in an already concentrated market) to move by 100 points or more.
The following table shows the HHI for the same industries previously reported.

Industry
Automotive Vehicles 2754.0
Breakfast Cereal 2521.3
Computer & Peripherals 1073.3
Fiber Optics 1517.2
Industrial Gas 1218.4
Plastic Bottles 628.1
Plastic & Rubber Products 32
Printing Ink 1177.4
Poultry 773.3

As you can see, the numbers from the HHI tell a similar story as those from the four-firm concentration ratio. However, it is important to remember that the ratio and index are just one tool that can be used and they are not without fault. One criticism of the four-firm concentration ratio is that by design it is deficient. Only four firms are used in the calculation of the ratio. Many industries have well over four firms, so looking at only four firms may not provide a complete picture of the industry. Another criticism is that the ratio does not account for shift in market share among the top four firms. If the top firm holds 30% market share and the fourth firm holds 15% one year and the following year the top firm drops to 23% and the fourth firm increases to 22% that would be something important to note. However when calculating the four-firm concentration ratio, the ratio would not change. An additional factor to consider is that foreign production is often excluded from the numbers and this could most certainly affect the concentration ratio especially in a market such as automotive manufacturing where much of the production is done overseas.

Multiple Choice
1. Industry sales for the 6 largest firms in the textile industry is as follows:
firm 1 30,000
firm 2 23,000
firm 3 15,000
firm 4 15,000
firm 5 8,000
firm 6 5,000
Total industry sales are 100,000. What is the four-firm concentration ratio?
a. .83
b. .96
c. 1
d. .68
The correct answer is a. By calculating the top 4 firm’s percent of industry sales and adding them, you get .30+.23+.15+.15= .83

2. Using the information provided in question 1, calculate the HHI.
a. 1743
b. 1879
c. 1968
d. 2000
The correct answer is c. By squaring each firms percent of sales and multiplying by 10,000, you get 1968.

3. Referencing questions 1 and 2, this industry is considered an oligopoly and moderately concentrated?
a.True
b. False
The correct answer is b, false. Although the four-firm concentration ratio of .83 does suggest this industry is an oligopoly, the HHI score of 1968 puts it in the concentrated category.

4. Which of the following is NOT a flaw/criticism of concentration indexes?
a. Narrow markets can give misleading ratios
b. In the past the HHI was used but today has no real-world application.
c. Geographic factors are often not taken into account.
d. The four-firm concentration ratio does not allow for shifts in market share.
The correct answer is b. While not perfect, the index is still widely used by statisticians, economists, and the US Department of Justice.

5. Because the newspaper industry has a four-firm concentration ratio of 22.1, it is very competitive.
a. True
b. False
The correct answer is b, false. The ratio in this case is deceptive. Newspapers are very localized and most often there is only 1-2 publications per city indicating very little local competition. The ratio is based on national newspaper carriers.

References

Domazlicky, Bruce, “From Theory to Reality: Concentration Ratios”, 2002
Duncan Bailey; Stanley E. Boyle,"The Optimal Measure of Concentration”,
Journal of the American Statistical Association, Vol. 66, No. 336 (Dec., 1971), pp. 702-706
Hart, P.E. “**Statistical Measures of Concentration vs. Concentration Ratios**”,
//The Review of Economics and Statistics// , Vol. 43, No. 1 (Feb., 1961), pp. 85-86
United States Department of Census, retrieved 10/13/07 http://www.census.gov/prod/ec02/ec0231sr1.pdf-
United States Department of Justice, retrieved 10/21/07 http://www.usdoj.gov/atr/public/testimony/hhi.htm