Topics in Production Theory PDF
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TOPICS IN PRODUCTION THEORY This volume is devoted to current topics in production theory. The papers are organized under four headings. Part I deals with technical change. Jorgenson reports on econometric research on production functions for a large number of production sectors as part of a general equilibrium model of an economy. F(Jrsund and Jansen focus on one industrial sector and study structural and technical change within the Norwegian aluminum industry, using Leif Johansens's concept of a short-run industry function. Kopp and Smith measure the effects of technical change on an even more disaggregated level. Two large-scale process analysis models provide a description of the production technology with the possibility of applying six specific process innovations. Baumol and Wolff outline a model which takes into account not only the contributions of R & D to the rate of growth of an economy's productivity, but also the likelihood that there is a relationship in the other direction. Part II is devoted to efficiency. Diewert uses a comparative static framework and duality theory to characterize two measures of the loss to the economy brought about by distortions in the resource allocation in the production sector. Fiire, Grosskopf and Lovell start out from Farrell's measure of productive efficiency and study nonparametric measurements of efficiency under less restrictive assumptions on technology. The papers in Part III deal with aggregation, quasi-fixed factors and cost of adjustment. Epstein addresses the problem of aggregating quasi-fixed factors in the context of an adjustment-cost model. Blackorby and Schwarm investigate the conditions under which - in adjustment-cost models - aggregates for heterogeneous capital and investment exist for individual firms and the conditions under which the sum of wealth functions over firms depends only on aggregate capital. Pindyck and Rotemberg model the industrial demand for structures, equipment and blue- and white-collar labor in a manner consistent with rational expectations and stochastic dynamic optimization in the presence of adjustment costs. Brown and Greenberg investigate the conditions under which the Divisia index of total factor productivity for all production units is path independent within a general equilibrium framework. Other aspects of production theory are present in Part IV. Vislie analyzes the optimal use of inputs for producing goods which take a long time to complete, when prices of inputs may change at some unknown future date. Bosworth and Pugh deal with the degree of capital utilization. In particular, increased utilization results in more rapid depreciation of the capital stock. Hamlin and Heathfield analyze consequences of the rate of profit being the maximand for a firm and examine ex ante employment, investment and shiftwork decisions in a putty-clay model when output and prices are given. Mizon and Nickell present estimates of a vintage production model for the U.K., with the aim of discovering whether it is possible to explain satisfactorily the output of manufacturing industries as a simple, stable function of a small number of input aggregates. In the same series Edited by Peter Bohm and Allen V. Kneese THE ECONOMICS OF ENVIRONMENT Edited by Jan Herin, Assar Lindbeck and Johan Myhrman FLEXIBLE EXCHANGE RATES AND STABILIZATION POLICY Edited by Steinar Str~m and Lars Werin TOPICS IN DISEQUILIBRIUM ECONOMICS Edited by Steinar Str~m and Bjorn Thalberg THE THEORETICAL CONTRIBUTIONS OF KNUT WICKSELL Edited by Steinar Str~m MEASUREMENT IN PUBLIC CHOICE Edited by Lars Matthiessen and Steinar Str;m UNEMPLOYMENT: MACRO AND MICRO-ECONOMIC EXPLANATIONS Edited by Lars Matthiessen THE IMPACT OF RISING OIL PRICES ON THE WORLD ECONOMY Edited by Lars Calmfors LONG-RUN EFFECTS OF SHORT-RUN STABILIZATION POLICY TOPICS IN PRODUCTION THEORY Edited by Finn R. F~rsund Department of Economics University of Oslo, Norway M Palgrave Macmillan ISBN 978-1-349-07125-8 ISBN 978-1-349-07123-4 (eBook) DOI 10.1007/978-1-349-07123-4 © The Scandinavian Journal of Economics, 1983, 1984 Softcover reprint of the hardcover 1st edition 1984 978-1-349-07123-4 All rights reserved. No part of this publication may be reproduced or transmiued, in any form or by any means, without permission This collection was originally published in The Scandinavian Journal of Economics, Vol. 85, 1983, No. 2 First published in book form 1984 by THE MACMILLAN PRESS LTD London and Basingstoke Companies and representatives throughout the world British Library Cataloguing in Publication Data Topics in production theory. I. Industrial productivity I. Ftilrsund, Finn R. 330 HC260.15Z ISBN 978-0-333-36554-0 Contents Contributors' Affiliations VI Part I Technical Change Dale W. Jorgenson: Modeling Production for General Equilibrium Analysis Finn R. F¢rsund and Eilev S. Jansen: Technical Progress and Structural Change in the Norwegian Primary Aluminum Industry 13 Raymond Kopp and V. Kerry Smith: Neoclassical Modeling of Nonneutral Technological Change: An Experimental Appraisal 27 William J. Baumol and Edward Wolff· Feedback from Productivity Growth to R & D 47 Part II Efficiency W. Erwin Diewert: The Measurement of Waste within the Production Sector of an Open Economy 59 Rolf Fiire, Shawna Grosskopf and C. A. Knox Lovell: The Structure of Technical Efficiency 81 Part III Aggregation, Quasi-fixed Factors and Cost of Adjustment Larry G. Epstein: Aggregating Quasi-fixed Factors 91 Charles Blackorby and William Schworm: Aggregating Heterogeneous Capital Goods in Adjustment-cost Technologies 107 Roberg S. Pindyck and Julio J. Rotemberg: Dynamic Factor Demands under Rational Expectations 123 Murray Brown and Richard Greenberg: The Divisia Index of Technological Change, Path Independence and Endogenous Prices 139 Part IV Other Aspects John Vislie: On the dynamics of Production under Cost Uncertainty 149 Derek Bosworth and Clive Pugh: Production and Maintenance; Joint Activities of the Firm 167 Alan Hamlin and David Heathfield: Shiftwork and the Choice of Technique under Alternative Maximands 183 Grayham Mizon and Stephen Nickell: Vintage Production Models of U.K. Manufacturing Industry 195 Contributors' Affiliations Dale W. Jorgenson Harvard University, Cambridge, MA Finn R. F~rsund University of Oslo, Norway Eilev S. Jansen Central Bureau of Statistics, Oslo, Norway Raymond Kopp Resources for the Future, Washington, DC V. Kerry Smith University of North Carolina, Chapel Hill, NC William J. Baumol Princeton University, Princeton, NJ and New York University, NY Edward Wolff New York University, NY W, Erwin Diewert University of British Columbia, Vancouver, BC Rolf Fare Southern Illinois University, Carbondale, IL Shawna Grosskopf Southern Illinois University, Carbondale, IL C. A. Knox Lovell University of North Carolina, Chapel Hill, NC Larry G. Epstein University of Toronto, ON Charles Blackorby University of British Columbia, Vancouver, BC William Schwarm University of British Columbia, Vancouver, BC Robert S. Pindyck M.I.T., Cambridge, MA Julio J. Rotemberg M.I.T., Cambridge, MA Murray Brown State University of New York, Buffalo, NY Richard Greenberg State University of New York, Buffalo, NY Jon Vislie University of Oslo, Norway Derek Bosworth Loughborough University, Leicestershire, England Clive Pugh Loughborough University, Leicestershire, England Alan Hamlin University of Southampton, England David Heathfield Unversity of Southampton, England Grayham Mizon University of Southampton, England Stephen Nickell London School of Economics and Political Science, London, England PART I TECHNICAL CHANGE Modeling Production for General Equilibrium Analysis Dale W. Jorgenson Harvard University, Cambridge, MA, USA Abstract The purpose of this paper is to present econometric models of producer behavior suitable for incorporation into a general equilibrium model. Implementation of these models requires a time series of inter-industry transactions tables. Second, implementation requires methods for estimation of parameters in systems of nonlinear simultaneous equations. Finally, the econom ic theory of producer behavior implies equality and inequality restrictions on the parameters that must be incorporated into the estimation. We discuss an empirical application to modeling producer behavior in thirty-six industrial sectors of the U.S. economy. I. Introduction The purpose of this paper is to present nonlinear econometric models of producer behavior suitable for incorporation into a general equilibrium model of the U.S. economy. General equilibrium modeling originated with the seminal work of Leontief (1941), based on empirical implementation of a static input-output model for the U.S. economy. Leontief (1953) gave a further impetus to the development of general equilibrium modeling by introducing a dynamic input-output model. The usefulness of the "fixed coefficients" assumption that underlies input-output analysis is hardly subject to dispute. By linearizing technology Leontief was able to solve at one stroke the two fundamental problems that arise in the practical implementation of general equilibrium models. First, the resulting general equilibrium model could be solved as a system of linear equations with constant coefficients. Second, the unknown parame ters describing technology could be estimated from a single data point. The first successful implementation of an applied general equilibrium model without the fixed coefficients assumption of input-output analysis is due to Johansen (1960). Johansen retained the fixed coefficients assumption in modeling demands for intermediate goods, but employed linear logarith mic or Cobb-Douglas production functions in modeling the substitution between capital and labor services and technical change. Linear logarithmic production functions imply that relative shares of inputs in the value of output are fixed, so that the unknown parameters 2 D. W. Jorgenson characterizing substitution between capital and labor inputs can be estimat ed from a single data point. In describing producer behavior Johansen employed econometric methods only in estimating constant rates of techni cal change. To implement models of producer behavior that are less restrictive than those of Johansen, it is essential to employ econometric methods. A possi ble econometric extension of Johansen's approach would be to estimate elasticities of substitution between capital and labor inputs along the lines suggested by Arrow, Chenery, Minhas, and Solow (1961). Unfortunately, constant elasticity of substitution production functions cannot easily be extended to encompass substitution among capital, labor, and intermediate inputs or among different types of intermediate inputs. With more than two inputs Uzawa (1%2) and McFadden (1963) have shown that constant elasticities of substitution imply, essentially, that all elasticities of substitu tion must be the same. An alternative approach to modeling producer behavior for general equi librium models is through complete systems of input demand functions for each industrial sector. Each system gives quantities of inputs demanded as functions of prices and output. This approach to modeling producer behav ior has been implemented by Berndt and Jorgenson (1973), Hudson and Jorgenson (1974), and Jorgenson and Fraumeni (1981). As in the description of technology by Leontief and Johansen, production is characterized by constant returns to scale in each sector. As a consequence, commodity prices can be expressed as functions of factor prices, as in the general equilibrium model of Samuelson (1953). This greatly facilitates the calcula tion of a set of equilibrium prices by permitting a substantial reduction in dimensionality of the space of unknown prices. The implementation of econometric models of producer behavior re quires a time series of inter-industry transactions tables. By comparison the noneconometric approaches of Leontief and Johansen require only a singel inter-industry transactions table. Second, the implementation of systems of input demand functions requires methods for the estimation of parameters in systems of nonlinear simultaneous equations. Finally, the incorporation of restrictions implied by the economic theory of producer behavior re quires estimation under both equality and inequality constraints. II. Producer Behavior In this section we present an econometric model of producer behavior that has been implemented for thirty-six industrial sectors of the U.S. economy by Jorgenson and Fraumeni (1981). This model is based on a production function for each sector, giving output as a function of inputs of intermedi ate goods produced by other sectors and inputs of the primary factors of Modeling production for general equilibrium analysis 3 production, capital and labor services. Output also depends on time as an index of the level of technology. Producer equilibrium under constant returns to scale implies the existence of a sectoral price function, giving the price of output as a function of the input prices and time. To incorporate the restrictions implied by the economic theory of producer behavior we gener ate our econometric model from a price function for each sector. Sectoral price functions must be homogeneous of degree one, nonde creasing, and concave in input prices. In addition, we assume that these price functions are homothetically separable in the prices of capital, labor, energy, and materials inputs. Under homothetic separability our model of producer behavior is based on a two-stage allocation process.1 In the first stage the value of sectoral output is allocated among capital, labor, energy, and materials inputs. In the second stage the value of each of the inputs is allocated among individual types of that input. Two-stage allocation makes it possible to determine the rate of technical change and the shares of thirty six intermediate goods and two primary factors of production in the value of output as functions of input prices. Our most important conceptual innovation is to determine the rate of technical change and the distributive shares of productive inputs simulta neously as functions of relative prices. While technical change is endog enous in our models of production and technical change, these models must be carefully distinguished from models of induced technical change, such as those analyzed by Hicks (1932), Kennedy (1964), Samuelson (1965), von Weizacker (1962) and many others .Z In those models the biases of technical change are endogenous and depend on relative prices. In our models the biases of technical change are fixed, while the rate of technical change is endogenous and depends on relative prices. As Samuelson (1965) has pointed out, models of induced technical change require intertemporal optimization, since technical change at any point of time affects future production possibilities. In our models myopic decision rules can be derived by treating the price of capital input as a rental price for capital services, even though the rate of technical change is endogenous.3 The rate of technical change at any point of time is a function of relative prices, but does not affect future production possibilities. This 1 Two-stage allocation is discussed by Blackorby, Primont and Russell (1978), especially pp. 103-216; they give detailed references to the literature. 2 A review of the literature on induced technical change is given by Binswanger (1978 a). Binswanger distinguishes between models, like ours and those of Ben-Zion and Ruttan (1978) Lucas (1967) and Schmookler (1966), with an endogenous rate of technical change and models, like those of Hicks (1932), Kennedy (1964), Samuelson (1965), von Weizsiicker (1962) and others, with an endogenous bias of technical change. Additional references are given by Binswanger (1978a). 3 For further discussion of myopic decision rules, see Jorgenson (1973).
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