The Herfindahl Index in Theory and Practice

• DOI: 10.1177/0003603X8503000405
• Date: 01 December 1985
• Published date: 01 December 1985
• Author: John E. Kwoka
• Subject Matter: Article

The Antitrust Bulletin/Winter

1985

The Herfindahl index in theory

and practice

BY

JOHN

E. KWOKA,

JR.

*

I.

Introduction

915

As a measure of market concentration, the Herfindahl index' for

some time has enjoyed a generally favorable reputation among

industrial organization economists and public-policy analysts. In

his recent comparison

of

alternative concentration measures,

Schmalensee takes the Herfindahl as a standard against which

others are judged.' Areeda and Turner state that compared to the

concentration ratio, the Herfindahl index "seems superior in

most respects, although both have deficiencies. . .

."3

The rea-

Professor of Economics, George Washington University.

AUTHOR'S NOTE: This

research

was funded by the Federal

Trade

Commission under contract

H5199.

The views expressed herein are

solely the author's.

Despite his legitimate prior claim, Hirschman appears to have

lost his case for naming the index. See A. O. Hirschman, "The

Paternity of an Index," 54 American Economic Review 761 (1964). This

article follows current convention.

2Richard Schmalensee, "Using the H-Index of Concentration

With Published Data," 59 Review

of

Economics and Statistics

186-93

(1977).

3Philip Areeda and Donald Turner, Antitrust Law (Boston: Little,

Brown, 1980), , 913.

©1986by Federal Legal Publications. Inc.

916 The antitrust bulletin

soning behind these views is not hard to fathom. First, the

Herfindahl can claim roots in oligopoly theory, a conceptual basis

lacking for most other measures

of

concentration. Second, the

index summarizes information about the entire distribution

of

firm sizes rather than providing more limited information only

about leading firms. Despite these attractive properties of the

Herfindahl index, until recently the ready availability (in the

Census

of

Manufactures

4)

of

the four-firm concentration ratio

was decisive. The new Justice Department Merger Guidelines,'

however, no longer measure industry structure by the concentra-

tion ratio,

but

by the Herfindahl. This methodological shift, plus

ongoing interest in the index, motivates this inquiry.

The present article is a systematic assessment

of

the theoreti-

cal and empirical foundations of the Herfindahl index. In addi-

tion, some new empirical work is presented, including abrief

examination

of

the revised Merger Guidelines. Our basic criteria

for evaluating the Herfindahl are contained in Stigler's dictum:

There are, in fact, two converging routes by which a measure

of

concentration

may

usefully be developed. The first route is to

develop a theory which relates the probability

of

competitive be-

havior to measurable aspects

of

the firm structure,

and

the second

route is to choose ameasure which correlates well with observable

indexes

of

competitive behavior,"

Section II

of

this article begins by discussing the purposes of any

concentration measure and detailing the particular properties of

the Herfindahl index. In Section III, the oligopoly theories that

constitute the basis for the Herfindahl are reviewed to determine

how plausible and general their insights are. Section IV turns to

empirical work, evaluating the literature that has employed the

4U.S. Bureau

of

the Census, Census

of

Manufactures (Washing-

ton,

D.C.:

USGPO,

various years).

U.S.

Department

of

Justice Merger Guidelines (June 14, 1982,

and

June

14, 1984).

6George Stigler, ed.,

"The

Measurement

of

Concentration," in

Organization

of

Industry (Homewood, Ill.: Richard D. Irwin, 1968), p.

30.

Herfindahl index :917

Herfindahl index to explain industry performance. In Section

V,

new research findings testing various model specifications with

the Herfindahl are reported. Finally, Section VI summarizes the

analysis

and

draws the general conclusion

that

whatever the

limitations

of

more conventional measures

of

concentration,

neither theory nor empirical work (Stigler's "converging routes")

provides grounds for preferring the Herfindahl index.

II. Purposes and properties

There is no basis for evaluating alternative concentration

measures without aclear understanding

of

the purpose they are

intended to serve. Again, Stigler's assertion is apropos:

"The

purpose

of

ameasure

of

concentration is to predict the extent

of

departure

of

price (or alternatively,

of

rate

of

return) from

the

competitive level.:" The mere description

of

the level

of

or change

in concentration in a particular market cannot be the ultimate

purpose.

That

exercise presumably is motivated by a concern over

the competitive performance, or changes in the competitive per-

formance,

of

the industry. Hence, one cannot decide among

concentration measures simply by analyzing their intrinsic prop-

erties. Ultimately, their value derives from theory or empirical

work

that

demonstrates their ability to capture features

of

the

size distribution

of

firms that are relevant to questions

of

com-

petitive performance.

These observations suffice to dispose

of

aconsiderable body

of

literature

that

has attempted to

put

the measurement

of

concentration on an axiomatic basis." Axioms are advanced as

7

[d.

8This literature begins with Marshall Hall and Nicholaus Tide-

man, "Measures of Concentration," 62 Journal

of

the American Statis-

tical Association

162-68

(1967), and includes the following subsequent

work: Christian Marfels,

"On

Testing Concentration Measures," 32

Zeitschrift

fur

Nationaloekonomie 461-86 (1972);

John

Hause, "The

Measurement of Concentrated Industrial Structure and the Size Distri-

bution of Firms," 6Annals

of

Economic and Social Measurement