Using the Herfindahl Index to Measure Concentration

• Author: David S. Weinstock
• DOI: 10.1177/0003603X8202700201
• Published date: 01 June 1982
• Date: 01 June 1982
• Subject Matter: Article

The Antitrust Bulletin/Summer 1982 285

Using the Herfindahl Index to measure

concentration

BY

DAVID

S. WEINSTOCK·

For many years, the

"top

four" (CR41)analysis has been the most

widely accepted method for determining the degree

of

concentra-

tion in a market. However, the CR4 approach has two significant

drawbacks. First, it does not take account

of

the relative sizes

of

the four leading companies. Thus, a market in which each

of

the

four largest firms has

20070

of

the market will show the same

degree

of

concentration as another market in which the top four

firms have shares

of

55070,

20070,

4070,

and

1070,

respectively. In

each case, the ratio will be

80070.

But, four equal-size firms may

compete with each other differently than four firms

of

disparate

size.

The second problem with the CR4 analysis is that it does not

take into account the total number

of

firms in the market, nor the

market shares

of

the companies below the four largest.

•Member, New York Bar.

I"CR4" is an abbreviation for "Concentration Ratio for the Top 4

Firms." Similarly, "CRX" refers to the concentration ratio for the top X

firms; "CR" alone willbe used to indicate the general method employed

in this measure, i.e., adding the market shares of the larger firms in a

market. "CR analysis" refers to an analysis of concentration of a

market using a CR approach.

©1982by Federal LegalPublications, Inc.

286 The antitrust bulletin

The Herfindahl Index' (H Index or H value) is calculated by

adding the square

of

each firm's market share.' The H value has a

theoretical range

of

close to 0.00 (in a market composed

of

an

2

The

Herfindahl

Index

is

named

for

Orris

Clemens

Herfindahl,

who

in 1950-1951 utilized this tool in analyzing

the

steel industry. In

1951 he was

awarded

a

Ph.D.

in Economics by

Columbia

University

for

his dissertation entitled

"Concentration

in

the

Steel Industry," in which

he examined

the

impact

that

the

formation

of

U.S.

Steel

had

on

the

steel

market

as a whole. Dr.

Herfindahl's

thesis advisor was

George

Stigler,

whose

work

in

the

field

of

industrial

organization

is highly

regarded.

Dr.

Herfindahl

died

on

December 16, 1972, at

the

age

of

54.

For

additional

biographical

material

see

BROOKS,

RESOURCE

ECONOMICS:

SELECTED

WORKS

OF

ORRIS

C.

HERFINDAHL,

ix-xxx (1974).

The

Herfindahl

Index

may

be

misnamed.

Six years

before

Dr.

Herfindahl

was

awarded

his

Ph.D.,

Albert

O.

Hirschman

described

the

characteristics

of

another

mathematical

tool-the

"Gini

Coefficient"

or

"Gini

Index"

-which

is merely

the

square

root

of

the

Herfindahl

Index

(i.e.,

the

Herfindahl

Index is actually

the

square

of

the

Gini Index). As a

result,

some

commentators

refer to this

measure

of

concentration

as

the

Herfindahl-Hirschman

Index

(HHI).

The

argument

over

who

is

the

actual

"creator"

of

the

Gini

and

Herfindahl

Indexes is discussed in

Hirschman,

The Paternity

of

an Index, 54 THE

AMERICAN

ECONOMIC

REVIEW

761 (September 1964).

The

following materials

on

the

Herfindahl

Index

are

included

for

the

possible use

of

the

reader:

AREEDA

&

TURNER,

ANTITRUST

LAW

74-80

(1980); Bailey &Boyle, The Optimal Measure

of

Concentration, 66 THE

JOURNAL

OF

THE

AMERICAN

STATISTICAL

ASSOCIATION

702-05 (December

1971); Pelster &Strangle, New Antitrust Chief and Herflndahl Index,

185

NEW

YORK

LAW

JOURNAL

1

(March

17, 1981);

SCHERER,

INDUSTRIAL

MARKET

STRUCTURE

AND

ECONOMIC

PERFORMANCE

58 (2d

ed.

1980);

Schmalensee, Using the H-Index

of

Concentration With Published

Data, 59

REVIEW

OF

ECONOMICS

AND

STATISTICS

186-93 (1976);

SINGER,

ANTITRUST

ECONOMICS:

SELECTED

LEGAL

CASES

AND

ECONOMIC

MODELS

136-55 (1968);

and,

STIGLER,

THE

ORGANIZATION

OF

INDUSTRY

29-37,

261-71 (1968).

See also

Ordover

&Willig,

American

Bar

Association,

Antitrust

Section,

Background

Papers

Re: Merger Guidelines, ch. 7

("Herfindahl

Concentration

Index")

(unpublished revised

draft

of

April

28, 1981);

and

Edwards

&Van

Buskirk,

The

Herfindahl

Index Revisited (un-

published

draft

of

September

11, 1981).

3

The

mathematical

formulas

utilized in

the

Herfindahl

Index

may

be

found

in

the

Appendix

infra.