Table Of ContentNations and Households
in Economic Growth
Essays in Honor of Moses Abramovitz
Edited by PAUL A. DAVID
DEPARTMENT OF ECONOMICS
STANFORD UNIVERSITY
STANFORD, CALIFORNIA
MELVIN W. REDER
DEPARTMENT OF ECONOMICS
THE CITY UNIVERSITY OF NEW YORK
NEW YORK, NEW YORK
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Library of Congress Cataloging in Publication Data
Main entry under title:
Nations and households in economic growth.
Includes bibliographies.
CONTENTS: Microeconomic foundations: Arrow, K. J.
The measurement of real value added.-David, P. A.
Fortune, risk, and the microeconomics of migration. -
Easterlin, R. A. Does economic growth improve the human
lot? [etc.]
1. Microeconomics—Addresses, essays, lectures.
2. Macroeconomics-Addresses, essays, lectures.
3. Economic policy-Addresses, essays, lectures.
I. Abramovitz, Moses, Date II. David, Paul A.,
ed. III. Reder, Melvin Warren, Date ed.
HB34.N36 330.1 73-5308
ISBN 0-12-205050-9
PRINTED IN THE UNITED STATES OF AMERICA
list of Contributors
Numbers in parentheses indicate the pages on which the authors' contributions begin.
KENNETH J. ARROW (3), Department of Economics, Harvard University,
Cambridge, Massachusetts
RUSSELL J. CHEETHAM (239), International Bank for Reconstruction
and Development, Washington, D. C.
PAUL A. DAVID (21), Department of Economics, Stanford University,
Stanford, California
RICHARD A. EASTERLIN (89), Department of Economics, The Wharton
School, University of Pennsylvania, Philadelphia, Pennsylvania
MILTON FRIEDMAN (265), Department of Economics, University of
Chicago, Chicago, Illinois
ELI GINZBERG (279), Graduate School of Business, Columbia University,
New York, New York
BERT G. HICKMAN (291), Department of Economics, Stanford University,
Stanford, California
ALLEN C. KELLEY (239), Department of Economics, Duke University,
Durham, North Carolina
SIMON KUZNETS* (127), Department of Economics, Emeritus, Harvard
University, Cambridge, Massachusetts
RONALD I. McKINNON (315), Department of Economics, Stanford
University, Stanford, California
DONALD J. MATHIESON (315), Department of Economics, Columbia
University, New York, New York
* Correspondence should be addressed to 67 Francis Avenue, Cambridge, Massachusetts.
XI
xii LIST OF CONTRIBUTORS
GEOFFREY H. MOORE* (333), Bureau of Labor Statistics, United States
Department of Labor, Washington, D.C.
MELVIN W. REDER (147), Department of Economics, Graduate Center,
City University of New York, New York, New York
WARREN C. SANDERSON (173), Department of Economics, Stanford
University, Stanford, California
TIBOR SCITOVSKY (223), Department of Economics, Stanford University,
Stanford, California
LORIE TARSHIS (361), Scarborough College, University of Toronto, West
Hill, Ontario, Canada
BRINLEY THOMAS (383), Department of Economics, University College,
Cardiff, United Kingdom
JEFFREY G. WILLIAMSON (239), Department of Economics, University
of Wisconsin, Madison, Wisconsin
* Present address: National Bureau of Economic Research, Inc., New York, New York.
Preface
The papers which form this book were pledged in celebration of Moses
Abramovitz's sixtieth birthday, on January 1, 1972.
By allowing the individual contributors perfect freedom in their choice of
subject matter, the editors happily have succeeded in marshalling a collection
whose range reflects the broad sweep of Abramovitz's recent interests within
the disciplines of economics and economic history. The individual and social
welfare significance of quantitative indices of economic growth, the mech-
anisms of economic-demographic interdependence and their bearing par-
ticularly upon "long swings" in the rate of growth, the changing role of
international relations in processes generating national economic development
and domestic economic instability—all these, and still other topics to which
Abramovitz's attention has turned, are treated in the present group of essays.
It is to be hoped that the volume as a whole will be accepted as a fitting
expression of appreciation of the exacting standards of scientific inquiry,
depth of insight, and modesty of exposition that continue to be the hallmarks
of Abramovitz's own scientific contributions.
These papers, however, cannot be expected to convey the warmth of
affection, nor the sincerity of admiration felt for an exemplary human being.
Yet such sentiments, no less than those of scholarly respect, are shared by all
who know Moses Abramovitz as a colleague, as a teacher, and as a friend.
P. A. DAVID
M. W. REDER
xiii
The Measurement
of Real Value Added
KENNETH J. ARROW
HARVARD UNIVERSITY
1. Introduction
The concept of "value added" has played an essential role in both private
and national income accounting, as a device for allocating the origins of income
to the various points in the productive sector of the economy at which primary
factors are brought to bear on the creation of the total value of final products.
It provides an accounting which exactly exhausts total product.
It is, however, a monetary magnitude and as such subject to all the vicis-
situdes which have made economists engage in the unavailing search for an
invariable standard of value. Variations in absolute and relative prices make
difficult meaningful comparisons of value added across space and time. Just
as we seek real measures of outputs and inputs, either by an index number of
quantities or by deflating monetary magnitudes by means of a suitable price
index, so it seems to be a reasonable goal to measure real value added in terms
of capital and labor or to deflate money value added, which may be thought of
as the money value of the net output of the industry, by some suitable index
number.
3
4 KENNETH J. ARROW
This search is indeed part of a larger aim, one which is purportedly achieved
by government statistical agencies, such as the Department of Commerce—
namely, the construction of a complete set of national income accounts in
real terms. It has, however, been argued convincingly by Stone and Prais
(1952) in an important but neglected paper that such a construction can never
be carried through with complete consistency. The inconsistencies are likely
to show7 up with special force in those items which represent differences between
well-defined flows—items such as value added or balance of payments. The
difficulties in using the "double-deflation" method are pointed up by Stone's
analysis. If money value added is the difference between the value of output
and the value of raw materials, then presumably real value added ought to be
the difference between the quantity of output and the quantity of raw materials.
This measurement has been used by Fabricant (1940, pp. 25 ff.) and Greary
(1944, p. 255). But as David (1962) has cogently pointed out, it is by no means
impossible that the double-deflation measure of real value added can lead to a
negative measurement.
To be sure, Sims (1969) has recently pointed out that the double-deflation
approach can be given a reasonable foundation if Divisia price indices rather
than fixed-base indices are used for the two deflations. In effect, only small
changes are considered, so that negative values cannot occur (since the value
added was necessarily positive in the base period).
To assess more deeply the relative merits of alternative measures of real
value added, it is necessary to ask what its economic meaning is, that is, what
we are trying to measure. I will argue first that the most natural meaning,
indeed the only one I can think of, arises from the estimation of production
functions. The output of any commodity is determined by the inputs of a
number of commodities, of which some are primary factors and others are
produced goods, which we will refer to as materials. The attribution of a special
role to primary factors, capital and labor, and the construction of an aggregate
for them can be justified only for the usual reasons: that their use in production
is separable from that of the materials. If Q is output of the commodity, and
K, L, and M stand for capital, labor, and materials, respectively, a production
function is a relation,
Q= Q(K,L,M).
Here, K, L, and M appear to play a symmetric role, and there is no apparent
reason to aggregate K and L rather than, say, K and M. The notion of real
value added has meaning in a production function framework only if this
relation can be assumed to take on the special nested form,
ß = QIV(K,L),M].
As is well known, this is equivalent to requiring that the marginal rate of
THE MEASUREMENT OF REAL VALUE ADDED 5
substitution between K and L in the production of Q is independent of M.
Metaphorically, we can imagine capital and labor cooperating to produce an
intermediate good, real value added (K), which in turn cooperates with
materials to produce the final product. This is an empirical and refutable
assumption about the nature of production functions. It would seem to be
reasonable for a broad variety of cases where the production process consists
of taking a mass of raw materials and transforming them into some finished
product, e.g., as in cotton spinning. The transformation may be accomplished
by varying combinations of capital and labor. But in other cases capital and
materials may seem to be a more natural aggregate, for example, in electric
power generating where increased capital expenditures basically serve to
economize on fuel. Without the separability assumption, however, it is hard
to assign any definite meaning to real value added, and probably the best thing
to say is that the concept should not be used when capital and labor are not
separable from materials in production.
Note that g, K, L, and M are observable variables, but V is not. In the
language sometimes used by statisticians, particularly those working with
psychological data, Kis a latent variable, while the others are manifest variables.
This remark has important implications. It shows that we can never hope to
achieve a unique measurement of V. If we determine any measurement of V
for which the nested form is valid, we can always find another in which the
magnitude of V is multiplied by some factor, and the marginal product of V
divided by the same factor.
In principle, it is possible to estimate a production function if one has
data on outputs and inputs over a sufficient variety of observations. If constant
returns to scale are assumed, something more is true: The equation of any
isoquant can be inferred from data on input quantities and input prices alone.
Hence, the whole production function can be reconstructed, even if output
is not directly measured, except that output is defined not uniquely but only
up to an arbitrary, multiplicative constant. Thus data on capital and labor
quantities and prices suffice to determine a production function for real value
added; this function could be thought of as a quantity index for real value
added.
Duality theory for production shows that another method is possible
with the same given data; it is possible to derive a price index which is inter-
preted as the minimum cost of producing one unit of real value added. Then
the latter can be obtained by using this price index to deflate nominal value
added.
The same general principles can be applied in a somewhat different way
to compute real value added in terms of output and materials (rather than in
terms of capital and labor). Here the prices of output and raw materials are
needed data. The quantity measure of real value added is an "external"
6 KENNETH J. ARROW
average of output and materials, that is, a function homogeneous of degree
one but decreasing in the quantity of materials.
For application to time series, it is also necessary to consider the possibility
that one or both of the production functions involved (relating gross output
to real value added and materials, or relating real value added to capital and
labor) have shifts in time. The problems raised here are no different than those
involved in estimating production functions when all variables are observable.
Independently of this work, Bruno (1972) has analyzed the concept of
value added using duality methods. His analysis is more thorough in some
respects, but does not overlap the results found here, its interests being
differently focused.
Remark. The discussion in this paper focuses on measuring real value
added in some one industry. No attempt is made to construct a complete
accounting framework in which real value added is comparable across
industries and can be summed to yield some measure of real national income.
Actually, this aggregation of real value added is of the same order of difficulty
as the aggregation of quantities of final goods. Money national income can be
written as the sum of money values of final commodities; then real national
income is some aggregate of the quantities of final commodities. Money
national income is also the sum of money values added for all industries; then,
if it is meaningful to measure real value added for each industry, it is meaningful
to construct real national income as an aggregate of real values added, with
the same problems of approximation as obtain in the measure of real national
income from final commodities.
2. Notation and Assumptions
We use the following notation: p will be a price, q a quantity, and the
following symbols are used as subscripts to/? and q.
0 output
v real value added
k capital
1 labor
m raw materials
Thus/7 is the price of capital and q the quantity of real value added. Finally,
k y
let Kbe value added in money terms. If there is a meaning to real value added,
then
V = pq. (1)
y y
Under constant returns, we also have
V = Pk<lvi+P\<1\ = Po^/o-P Q - (2)
m m
