Table Of ContentCONTRIBUTIONS
TO
ECONOMIC ANALYSIS
196
Honorary Editor:
J. TINBERGEN
Editors:
D. W. JORGENSON
J. WAELBROECK
NORTH-HOLLAND
AMSTERDAM · NEW YORK · OXFORD · TOKYO
PRICE LEVEL
MEASUREMENT
Edited by
W.E. DIEWERT
Department of Economics
The University of British Columbia
Vancouver, Canada
1990
NORTH-HOLLAND
AMSTERDAM · NEW YORK · OXFORD · TOKYO
ELSEVIER SCIENCE PUBLISHERS B.V.
Sara Burgerhartstraat 25
P.O. Box 211, 1000 AE Amsterdam, The Netherlands
Sole distributors for the United States:
ELSEVIER SCIENCE PUBLISHING COMPANY, INC.
655 Avenue of the Americas
New York, N.Y. 10010, U.S.A.
ISBN: 0 444 88108 5
© Minister of Supply and Services Canada, 1990
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or trans-
mitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise,
without the prior written permission of the publisher.
Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright
Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about
conditions under which photocopies of parts of this publication may be made in the U.S.A. All other
copyright questions, including photocopying outside of the U.S.A., should be referred to the publisher,
unless otherwise specified.
No responsibility is assumed by the publisher for any injury and/or damage to persons or property as
a matter of products liability, negligence or otherwise, or from any use or operation of any methods,
products, instructions or ideas contained in the material herein.
PRINTED IN THE NETHERLANDS
INTRODUCTION TO THE SERIES
This series consists of a number of hitherto unpublished studies, which are intro-
duced by the editors in the belief that they represent fresh contributions to economic
science.
The term "economic analysis" as used in the title of the series has been adopted
because it covers both the activities of the theoretical economist and the research
worker.
Although the analytical methods used by the various contributors are not the same,
they are nevertheless conditioned by the common origin of their studies, namely
theoretical problems encountered in practical research. Since for this reason, busi-
ness cycle research and national accounting, research work on behalf of economic
policy, and problems of planning are the main sources of the subjects dealt with, they
necessarily determine the manner of approach adopted by the authors. Their
methods tend to be "practical" in the sense of not being too far remote from appli-
cation to actual economic conditions. In additon they are quantitative.
It is the hope of the editors that the publication of these studies will help to stimulate
the exchange of scientific information and to reinforce international cooperation in
the field of economics.
The Editors
PRICE LEVEL MEASUREMENT - W.E. Diewert (Editor)
Canadian Government Publishing Centre /
Elsevier Science Publishers B.V. (North-Holland) 1
© Minister of Supply and Services Canada, 1990
AN OVERVIEW OF THE PAPERS ON PRICE LEVEL MEA-
SUREMENT
W.E. Diewert
The first theoretical paper is by Pollak, "The Theory of the Cost-of-Living Index". This
paper was originally issued by the U.S. Bureau of Labor Statistics as BLS Working
Paper 11 in June 1971. The paper has been extremely influential and is regarded as a
"classic" in the field by researchers in index number theory. Pollak not only develops the
theory of the cost-of-living index which the CPI approximates, he also studies the related
problem of measuring welfare. Some of the contributions that Pollak makes in this paper
are: (i) he provides a systematic theory of empirically implementable bounds for the
single consumer cost-of-living index, (ii) he systematically develops the theory of the
Malmquist [1953] quantity or welfare index, and (iii) he brings out the connection
between functional forms for a consumer's welfare or utility function and the functional
form for the corresponding cost-of-living index.
The paper by Diewert, "The Theory of the Cost-of-Living Index and the Measurement
of Welfare Change", continues to develop the theoretical foundations of CPI. Drawing
on Pollak [1981], Diewert develops the many-consumer theory of the cost-of-living index.
Diewert adapts a technique due originally to Koniis [1924] and shows that many theoretically
unobservable indexes may be bounded by empirically computable Paasche and Laspeyres
indexes. He also discusses several other issues from a theoretical perspective, including:
(i) the use of the chain principle versus the fixed base principle in constructing index
numbers, (ii) the problems involved in constructing group welfare indexes, (iii) the con-
struction of subindexes and how they may be combined to form an overall index and (iv)
the treatment of housing and other consumer durables in the CPI.
2 W.E. Diewert
The paper by Jorgenson and Slesnick, 'Individual and Social cost of Living Indexes",
is an intellectual tour de force as Russell notes in his perceptive comments on the paper.
It is not possible to summarize accurately the entire paper in this brief introduction; however,
some of the major ideas in the paper can be mentioned here. The core of the Jorgenson-
Slesnick paper is an econometric model of aggregate consumer behavior which is based
on Lau's [1977] theory of exact aggregation which in turn (greatly) generalizes the aggregate
model oi consumer behavior implemented by Berndt, Darrough and Diewert [1977]. The
basic idea is that each household is assumed to have the same preferences (apart from a
stochastic term) once we standardize for various demographic characteristics or attributes
such as family size, age of head, region of residence, race, rural versus urban, etc. By shrewd-
ly choosing the functional form for the household preferences, Jorgenson and Slesnick
end up with a system of aggregate consumer demand functions that depend on consumer
prices, the distribution of income, and the distribution of household characteristics. Given
aggregate time series and some cross section data the parameters which characterize the
household preferences may be estimated econometrically and this is done in Jorgenson,
Lau and Stoker [1982]. Once household preferences are known, individual cost-of-living
or welfare indexes may be calculated as well as aggregate indexes. Jorgenson and Slesnick
also compare their "econometric" approach to the construction of aggregate cost-of-living
and social welfare indexes to the "exact" index number approach outlined in the earlier
paper by Diewert. There are advantages and disadvantages to each approach. One disad-
vantage of the Jorgenson-Slesnick approach is that new time series information would lead
to new econometric estimates of the household preference parameters and hence new
historical index numbers would have to be calculated. However, there is much to be prais-
ed in the Jorgenson-Slesnick approach as Russell notes in his comment.
Riddell in his paper, "Leisure Time and the Measurement of Economic Welfare" ex-
tends the traditional theory of the cost-of-living index to incorporate the consumer-worker's
labour supply (or leisure choice) decision. He also empirically implements his approach
using Canadian per capita data. He compares his approach with the traditional approach
(which neglects the labour supply decision) and finds that real income growth is dramatically
slower in Canada when the labour supply decision is taken into account. It should also
be mentioned that Riddell's approach takes into account income taxes as well as commodity
taxes. Thus if the government decreased commodity taxes and increased income taxes in
Overview of the papers 3
a neutral manner, Riddell's welfare indicator would show no change whereas a "tradi-
tional" welfare indicator (such as per capita national income deflated by the CPI) would
show an increase. Riddell also extends and empirically implements the Pencavel [1977] -
Cleeton [1982] theory of real wage indexes.
In the paper, "Preference Diversity and Aggregate Economic Cost-of-Living Indexes",
Blackorby and Donaldson look for conditions on the preferences of individual consumers
that are sufficient to ensure that an aggregate cost-of-living index is independent of the
distribution of utilities or real incomes of the households in the economy. Their results
are interesting but essentially negative: it appears that individual household preferences
must be homothetic in order for the aggregate cost-of-living index to be independent of
the distribution of utilities. Of course, homothetic preferences must be rejected on em-
pirical grounds since homothetic preferences imply unitary income elasticities for all goods
(which contradicts Engel's Law).
Eichhorn and Voeller in their paper, "The Axiomatic Foundations of Price Indexes and
Purchasing Power Parities", outline the "axiomatic" or "test" approach to index number
theory, as opposed to the "economic" approach which was followed by the earlier papers
from Pollak to Blackorby and Donaldson. In his comments on Eichhorn and Voeller,
Blackorby explains the difference between the "test" approach and the "economic" ap-
proach to a price index: in the former approach, prices and quantities in both periods are
taken to be independent variables whereas in the latter approach, quantities are regarded
as dependent variables. It should be mentioned that Diewert in his paper "The Theory
of Cost-of-Living Index and the Measurement of Welfare Change" provides an axiomatic
characterization of the "economic" approach to the cost-of-living index. In defence of
Eichhorn and Voeller's approach, it should be noted that the "economic" approach to
the cost-of-living index followed by most authors in this volume may not be the correct
one. The "economic" approach to index number theory rests on the assumption of utility
maximizing behaviour which may or may not be true. If it is not true, then there is a need
for an alternative theoretical foundation for the CPI, and the "axiomatic" approach
developed by Eichhorn and Voeller can fill this need.
4 W.E. Diewert
References to papers not in this volume
Berndt, E.R., W.E. Diewert and M.N. Darrough [1977], "Flexible Functional Forms and
Expenditure Distributions: An Application to Canadian Consumer Demand Functions",
International Economic Review 18, pp.651-675.
Cleeton, D.L. [1982], "The Theory of Real Wage Indices", American Economic Review
72, pp.214-225.
Lau, L.J. [1977], "Existence Conditions for Aggregate Demand Functions", Technical
Report No. 248, Institute for Mathematical Studies in the Social Sciences, Stanford
University, Stanford, California.
Jorgenson, D.W., L.J. Lau and T.M. Stoker [1982], "The Transcendental Logarithmic
Model of Aggregate Consumer Behavior", pp.97-238 in Advances in Econometrics, Vol.
1, R.L. Basmann and G.F. Rhodes Jr. (eds.), Greenwich: JAI Press.
Konus, A.A. [1924], "The Problem of the True Index of the Cost-of-Living", Translated
in Econometrica 1 [1939], pp. 10-29.
Malmquist, S. [1953], "Index Numbers and Indifference Surfaces", Trabajos de Estadistica
4, pp.209-242.
Pencavel, J.H. [1977], "Constant Utility Index Numbers of Real Wages", American
Economic Review 67, pp.91-100.
Pollak, R.A. [1975], "Subindexes of the Cost-of-Living Index", International Economic
Review 16, pp.135-150.
[1981], "The Social Cost-of-Living Index", Journal of Public Economics 15,
pp.311-336.
PRICE LEVEL MEASUREMENT - W.E. Diewert (Editor)
Canadian Government Publishing Centre /
Elsevier Science Publishers B.V. (North-Holland) 5
© Minister of Supply and Services Canada, 1990
THE THEORY OF THE COST-OF-LIVING INDEX
Robert A. Pollak*
Department of Economics
University of Pennsylvania
SUMMARY
In this paper I summarize the theory of the "cost-of-living index" and the closely related
theory of the "preference field quality index". The first section is devoted to notation and
preliminary background, and the second summarizes the theory of the cost-of-living in-
dex. The next two sections discuss upper and lower bounds for the index, and the preference
orderings for which these bounds are attained. In Section 5 I examine the effect on the
index of the choice of a base indifference curve. Section 6 examines the form of the cost-
of-living index corresponding to various specific preference orderings. In Sections 7 and
8 I examine the preference field quantity index, a quantity index which is conceptually
similar to the cost-of-living index. I show that it is equal to the expenditure index deflated
by the cost-of-living index if and only if the preference ordering is homothetic to the origin.
In Section 91 discuss the use of price indexes in empirical demand analysis and argue that
the cost-of-living index is inappropriate for this purpose.
6 R.A. Pollak
In this paper I summarize the theory of the "cost-of-living index" and the closely related
theory of the "preference field quality index". The first section is devoted to notation and
preliminary background, and the second summarizes the theory of the cost-of-living in-
dex. The next two sections discuss upper and lower bounds for the index, and the preference
orderings for which these bounds are attained. In Section 5 I examine the effect on the
index of the choice of a base indifference curve. Section 6 examines the form of the cost-
of-living index corresponding to various specific preference orderings. In Sections 7 and
8 I examine the preference field quantity index, a quantity index which is conceptually
similar to the cost-of-living index. I show that it is equal to the expenditure index deflated
by the cost-of-living index if and only if the preference ordering is homothetic to the origin.
In Section 9 I discuss the use of price indexes in empirical demand analysis and argue that
the cost-of-living index is inappropriate for this purpose.
There are a number of areas of practical and theoretical importance which I do not discuss
in this paper. No mention is made of quality change, goods provided by governments,
or the treatment of the environment. Goods are assumed to be perfectly divisible and tran-
saction costs to be zero. Intertemporal aspects of the consumer's allocation problem are
ignored, so the treatment of saving, interest rates, and consumer durables is not discussed.
I have ignored these areas not only because they are difficult but also because a systematic
theoretical attack on any of them must be based on a thorough understanding of the basic
theory. A major purpose of this paper is to present a rigorous survey of that theory. The
material in the first two sections should be familiar, but much of the material in later sec-
tions is new.
The discussion of bounds on the cost-of-living index in Sections 3 and 4 emphasizes the
importance of both upper and lower bounds. It is well known that the Laspeyres index
provides an upper bound to the cost-of-living index based on the indifference curve at-
tained in the reference situation, but little attention has been given to the corresponding
lower bounds. In Section 3 I establish upper and lower bounds, and in Section 4 I
characterize the preference orderings for which these bounds are attained.
It is well known that the cost-of-living index is independent of the base indifference curve
if and only if the indifference map is homothetic to the origin. In Section 5 I consider
