# How to Calculate the Herfindahl-Hirschman Index (HHI)

The Herfindahl-Hirschman Index (HHI) is a measure of the competition between firms and related industries. BusinessZeal will tell you how to calculate the Herfindahl-Hirschman Index (HHI).

BusinessZeal Staff

Quick Fact

The Herfindahl index is a commonly used measure for economic concentration. It is also used for portfolio diversification to find out the number of positions in a portfolio.

The Herfindahl index is a commonly used measure for economic concentration. It is also used for portfolio diversification to find out the number of positions in a portfolio.

HHI is one of the many economic concepts used to measure market shares. Within a market, there exist a number of firms that belong to the same industry. Every firm manufactures items and has a share in the market. If you have ever read financial reports, you must have come across terms, like 'healthy market share', 'market power', etc. The HHI is equal to the net summation of the total shares in the market. This value is used to determine the competition. In the paragraphs below, you will learn how to find HHI.

The Concept

- As already mentioned in the introduction, this value is an indication of the market concentration.
- Mathematically, it is expressed as the summation of the squares of all the individual market share percentages.
- It is also used in economic and technology management.
- Market shares are expressed in terms of percentages; if the whole percentages are taken for calculation, the HHI will range between 0 to 10,000. Otherwise, it can be expressed between 0 to 1.
- This value helps determine which company is in monopoly or if the market is fairly competitive.
- In an ideal, competitive market situation, the HHI should be close to zero, as the market share would be equally divided.
- If, however, only a single firm holds monopoly, then the HHI inches towards the 10,000 mark.
- According to experts, an HHI value of less than 1,000 indicates good competition, a value between 1,000 to 1,800 indicates moderate concentration, and a value greater than 1,800 indicates high concentration.
- If the market shares are equal, you can directly multiply the number of firms by the square of the market share and derive the HHI.

HHI Formula

HHI = (s

_{i})^{2}+ (s_{i})^{2}+ (s_{i})^{2}+ . . . . . + (s_{i})^{2}where i = 1 ... N (N is the maximum number of firms)

HHI Calculator

Herfindahl-Hirschman Index

Steps to Calculate

Step I

Find out the value of 'N'. Consider the number of firms that are involved in the market share. Generally, the industry's largest 50 firms are considered.

Step II

Determine the market share of every firm.

Step III

Calculate the square of every value, i.e., every market share. If there are 5 firms involved, you need to find the square of every market share percentage and have 5 results in hand.

Step IV

Add all the squares together. This is your HHI value.

Examples

Example I

- Assume there are 5 stores: A, B, C, D, and E.
- Assume that their market share percentages are 40%, 15%, 15%, 10%, and 20%, respectively.
- Considering the formula, the HHI calculation will be as follows:

= 1600 + 225 + 225 + 100 + 400

= 2550

If the market has equal competition, the HHI should ideally approach zero. If it is a monopolized market, the HHI will be close to 10,000 (assuming n=50).

Example II

Consider 10 firms with unequal market shares.

Firm | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Market Share | 10 | 25 | 5 | 8 | 7 | 5 | 10 | 15 | 5 | 10 |

From the table above, HHI = 25^2 + 5^2 + 8^2 + 7^2 + 5^2 + 10^2 + 15^2 + 5^2 + 10^2

= 625 +25 + 64 +49 + 25 +100 + 225 +25 + 100

Therefore, HHI = 1238

In this case, the market is said to be moderately concentrated.

Calculation of HHI using MS Excel and Stata

- You can learn how to calculate the Herfindahl index in Excel.
- You can create a data table that takes input data from the user or imports data from another file (use the important option).
- The squares of the market share percentage values can be calculated separately using the 'Function wizard'.
- These values can be entered separately into the other cells, whose sum can be calculated using the 'Autosum' feature.
- Stata is a statistical software. It contains inbuilt modules that can help compute the HHI.

Some Vital Points

- The HHI value is very important to analyze how the market power can be enhanced.
- Since the different values signify different levels of market concentration, we will understand when and where the firm needs to improve or slow down or retain the current scenario.
- Experts state that if the HHI value increases by more than 200 points during mergers in a moderately concentrated market, it gives rise to an antitrust environment. It is believed that the merged company will reduce competition.
- The geographical location plays an important role while determining the HHI. It gives a clearer view regarding the perfectly competitive vs. monopoly market.
- A monopoly will have the maximum HHI value, since it has almost 100% of the company's market share.