Index Numbers: Essays in Honour of Sten Malmquist

285 Pages·1998·9.042 MB·English

by  Rolf Färe, Shawna Grosskopf (auth.), Rolf Färe, Shawna Grosskopf, R. Robert Russell (eds.)

INDEX NUMBERS: ESSAYS IN
HONOUR OF STEN
MALMQUIST
INDEX NUMBERS:
ESSAYS IN HONOUR OF
STEN MALMQUIST
EOITEO BY
Rolf Fare
Southern Illinois University at Carbondale
Carbondale, Illinois 62901
•
Shawna Grosskopf
Southern Illinois University at Carbondale
Carbondale, Illinois 62901
•
R. Robert Russell
University of California at Riverside
Riverside, California
....
"
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
Index numbers : essays in honor of Sten Malmquist / edited by Rolf
Făre, Shawna Grosskopf, R. Robert Russell.
p. cm.
"Selections of papers presented at the ArDe Ryde Symposium in honor
ofProfessor Sten Malmquist, held in Lund on May 28, 1996" --Pref.
Includes bibliographical references and index.
ISBN 978-94-010-6035-6 ISBN 978-94-011-4858-0 (eBook)
DOI 10.1007/978-94-011-4858-0
1. Economics, Mathematical--Congresses. 2. Index numbers
(Economics) --Congresses. 1. Malmquist, Sten, 1917- . II. Făre,
Rolf, 1942- . III. Grosskopf, Shawna. IV. Russell, R. Robert.
V. ArDe Ryde Symposium (1996: Lund, Sweden)
HB135.1547 1997
330'.0I'51--dc21 97-38202
CIP
Copyright © 1998 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 1998
Softcover reprint ofthe hardcover Ist edition 1998
AU rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, mechanical, photo
copying, recording, or otherwise, without the prior written permission of the
publisher, Springer Science+Business Media, LLC.
Printed on acid-free paper.
CONTENTS
Preface IX
Introduction 1
by Rolf Fare, Shawna Grosskopf and R. Robert Russell
ESSAY 1 7
DISTANCE FUNCTIONS IN CONSUMER AND PRODUCER
THEORY
by R. Robert Russell
1.1 Introduction 7
1.2 Distance-Function Representations of Technologies
or Preference Orderings 10
1.3 Distance Functions as Technical Efficiency Indexes 28
1.4 Duality and the Distance Function 45
1.5 Distance Functions and Index Numbers 64
1.6 Concluding Remarks 84
ESSAY 2 91
INPUT PRICE, QUANTITY, AND PRODUCTIVITY INDEXES
FOR A REVENUE-CONTRAINED FIRM
by Bert M. Balk
v
VI
2.1 Introduction 91
2.2 Primal and Dual Direct Representations of the
Technology 93
2.3 The Indirect Input Distance Function, Cost Function,
and Efficiency Measures 99
2.4 The Indirect Input Price Index and Quantity Index 104
2.5 The Indirect Input Based Productivity Indexes 116
2.6 Conclusion 124
ESSAY 3 127
MALMQUIST PRODUCTIVITY INDEXES: A SURVEY OF
THEORY AND PRACTICE
by Rolf Fare, Shawna Grosskopf and Pontus Roos
3.1 Introduction 127
3.2 Theory 128
3.3 Empirical Applications 151
3.4 Concluding Remarks 175
ESSAY 4 191
IMPLEMENTING THE MALMQUIST PRODUCTIVITY INDEX:
THE CASE OF THE NATIONAL CORPORATION OF SWEDISH
PHARMACIES
by Nils-Olov Norlander and Pontus Roos
4.1 Introduction 191
4.2 Implementation of Malmquist Productivity Indexes 195
4.3 Performance Indicators, Incentives, and Malmquist 206
Indexes
4.4 Concluding Remarks 211
Index Numbers: Essays
VII
ESSAY 5 217
MALMQUIST PRODUCTIVITY INDEXES: AN EMPIRICAL
COMPARISON
by Hans Bjurek, Finn R. F¢rsund and Lennart Hjalmarsson
5.1 Introduction 217
5.2 The Malmquist Indexes 221
5.3 Data 228
5.4 Empirical Results 229
5.5 Quo Vadis, Malmquist? 232
ESSAY 6 241
INPUT AND OUTPUT INDICATORS
by Robert G. Chambers
6.1 Introduction 241
6.2 Notation, Assumptions, and Definitions 242
6.3 Previous Work on Input and Output Indexes 247
6.4 Exponential Input and Output Indicators 253
6.5 Exact Measures of the Luenberger Exponential 255
Input and Output Indicators
6.6 Transitivity of Input and Output Indicators 258
6.7 Conclusion 269
APPENDIX 273
Contributors
INDEX 275
PREFACE
This book contains a selection of papers presented at the Arne Ryde
Symposium in honor of Professor Sten Malmquist, held in Lund on
May 28, 1996. The symposium was financed by the Arne Ryde
Foundation and organized by BjllJrn Thalberg, Lund University;
Rolf Fare, Southern Illinois University; and Pontus Roos, Institute
of Health Economics, Lund.
The Arne Ryde Foundation was founded in memory of Arne Ryde,
an exceptionally promising graduate student at the Department of
Economics at the University of Lund. He died after an automobile
accident in 1968 when he was only 23 years old. In his memory
his parent established the foundation for the advancement of re
search at the Departm~ht of Economics at the University of Lund.
The foundation finances international symposia in major fields of
economic research.
The papers at the symposium were offspring of Professor Malm
quist's work on index numbers. The symposium was honored by
the presence of Professor Malmquist, now Professor Emeritus at the
Department of Statistics at Stockholm University.
The manuscript has been prepared by Mariann Baratta; we thank
her for a job well done.
ix
INTRODUCTION
by
Rolf Fare, Shawna Grosskopf and R. Robert Russell
In 1952, Professor Sten Malmquist was appointed as an opponent
on Dr. Erland von Hoffsten's doctoral dissertation "Price Indexes
and Quality Changes," Uppsala Universitet. To facilitate his eval
uation of this dissertation, Professor Malmquist constructed the
now-famous Malmquist quantity index. In the course of formulat
ing the index, Malmquist developed a distance function defined on
a consumption space. This function, which is the consumer analog
to the Shephard input distance function of producers, was used in
ratio form to define the quantity index.
Out of Malmquist's opposition emerged the paper, "Index Numbers
and Indifference Surfaces." The paper was subsequently presented
at a statistical conference in Spain by Professor Hermand Wold,
who at the time had no paper ready for the conference. In 1953,
the paper was published in the Spanish statistical journal, Tmbajos
de Estadistica (Malmquist (1953)).
This volume contains papers based on Malmquist's contribution
some 47 years ago. Some of the papers are surveys or expositions
of the literature emanating from Malmquist's paper. Others are
original contributions to the ongoing research agenda inspired by
Malmquist's contribution.
Essay 1, by R. Robert Russell, is an exposition of the Malmquist
Shephard distance function and some of its uses in economic anal-
2 INTRODUCTION
ysis. The essay describes the role of the distance function as an
implicit representation of a (multiple output) technology (as well
as a consumer preference ordering) and argues that it is a natural
index of technical efficiency. The essay then develops the symmetric
duality between the distance function and the (producer) cost func
tion or (consumer) expenditure function. This essay also features
the original insight of Malmquist's paper, in which the distance
function is interpreted as a quantity index and a ratio of the dis
tance function evaluated at different points constitutes an elegant
index of the cost of living that is symetrically dual to the Konus
cost-of-living index. Finally, the essay also introduces the use of
the distance function in formulating productivity indexes measur
ing changes in productivity over time or relative productivity levels
of different production units. The emphasis of this exposition of the
distance function and its applications is on intuition, emphasizing
graphical illustrations, with references to the literature for proofs.
Essay 2, by Bert M. Balk, extends Malmquist's ideas to construct
input-price, quantity, and productivity indexes for revenue-con
strained producers-that is, firms that minimize cost subject to the
attainment of a target revenue. The theory of revenue-constrained
firms was developed by Fare and Grosskopf (1994) and has recently
been used by Fisher (1995) to model a small open economy. In
this essay, Balk lays out the basic duality theory that underlies the
construction of his indexes and provides new results on the approx
imation of price and quantity indexes by Fisher index numbers and
on the equivalence (under certain conditions) of his indexes and
Tornqvist index numbers. His productivity indexes capture the
effect of efficiency changes as well as technical change.
The third essay, jointly authored by Rolf Fare, Shawna Grosskopf,
and Pontus Roos, is a survey of the theoretical and empirical work
on Malmquist productivity indexes. On the theoretical side, the
survey includes a number of issues that have arisen since the Malm
quist productivity index was first proposed in the seminal paper by
Caves, Christensen and Diewert (1982). These issues include the
Index Numbers: Essays 3
definition of the Malmquist productivity index; although all are
based on the distance functions that Malmquist employed to for
mulate his original quantity index, variations include the geometric
mean form used by Fare, Grosskopf, Lindgren and Roos (1989) and
the quantity index form referred to by Diewert (1992) as Hicks
Moorsteen. This raises the issue of whether this index is a technol
ogy index or an index of total-factor productivity (in the average
product sense), which in turn raises the issue of the role of returns
to scale in specifying and computing the index. Other theoretical
issues discussed here include the relationship to the Tornqvist and
Fisher indexes, and the role of the circular test.
The survey of the empirical literature covers over 70 papers and is
divided into sections reviewing studies of the public sector, banking,
agriculture, countries and internationar comparisons, electric util
ities, transportation, and insurance. Recommendations concern
ing the specification, computation, and interpretation of Malmquist
productivity conclude this essay.
Essay 4 documents the ongoing implementation of Malmquist pro
ductivity indexes in the evaluation of the 800 member pharmacies
in the Corporation, and is authored by two of the participants in
that process, Nils-Olov Norlander (the Chief Controller of the Cor
poration) and Pontus Roos (the project manager at the Institute
for Health Economics). This essay highlights the symbiotic rela
tionship that has arisen during the process of this implementation:
issues raised by individual pharmacies and the administration of
the corporation became research topics in the development of the
index itself, including the role of quality, the connection to prof
itability, etc. This relationship emphasizes the fact that this index
is useful to industry as a performance tool precisely because it has
been developed within a production-theoretic framework.
In Essay 5, a trio of Scandinavians, Hans Bjurek, Finn F(Zlrsund,
and Lennart Hjalmarsson do an empirical comparison of various
formulations of Malmquist productivity indexes. The basic two