Nations 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 ® ACADEMIC PRESS New York and London 1974 A Subsidiary of Harcourt Brace Jovanovich, Publishers COPYRIGHT © 1974, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER. ACADEMIC PRESS, INC. Ill Fifth Avenue, New York, New York 10003 United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London NW1 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