The economics of the profit rate : competition, crises, and historical tendencies in capitalism 1852787600

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THE ECONOMICS OF THE PROFIT RATE Competition, Crises and Historical Tendencies in Capitalism

\\ GERARD DUMENIL Directeur de Recherche au CNRS, LAREA-CEDRA, Universite de Paris-X Nanterre, France

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DOMINIQUE LEVY Directeur de Recherche au CNRS, CEPREMAP, Paris, France

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©Gerard Dumenil and Dominique Levy 1993

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, eiectronic, mechanical, photocopying, recording, or otherwise without the prior permission of the publisher. Published by Edward Elgar Publishing Limited Gower House Croft Road Aldershot Hants GUll 3HR England Edward Elgar Publishing Company Old Post Road Brookfield Vermont 05036 USA British Library Cataloguing in Publication Data

Dumenil, Gerard Economics of the Profit Rate: Competition, Crises and Historical Tendencies in Capitalism. - (New Directions in Modern Economics Series) I. Title II. Levy, Dominique Ill. Series

338.5

ISBN 1 85278 760 O Printed and bound in Great Britain by Hartnolls Limited, Bodmin, Cornwall

Contents List of Figures Preface

PART I

Vll X1

THE PROFIT RATE

1. The Economics of the Profit Rate: A

Summary 2. Definitions and Measures of the Profit Rate PART II

3 19

COMPETITION AND PRICES OF PRODUCTION

3. Prices of Production 4. Long-Term Equilibrium in Classical and W alrasian Models 5. The Classical Analysis of Competition 6. Convergence?

35 50 69 82

PART III GENERAL DISEQUILIBRIUM 7. A General Disequilibrium Model 8. Development of the Basic Model 9. Proportions and Dimension in the Short and Long Terms 10. Out of the Mainstream

v

111 140 167 177

Contents

V1

PART IV STABILITY AND BUSINESS FLUCTUATIONS 11. The Real and Monetary Determinants of Macro (In)stability 12. The Impact of the Profit Rate on the Macroeconomy 13. Business Fluctuations in other Paradigms PART V 14. 15. 16. 17.

197 224 232

TECHNOLOGY AND DISTRIBUTION: A HISTORICAL PERSPECTIVE

The Historical Profile of the Profit Rate Historical Tendencies Accumulation and Growth Profitability Trends

245 262 285 295

PART VI HISTORY 18. Profitability and Management 19. A Chronological Overview 20. The Historical Dynamics of Capitalism

307 327 342

Historical Data (1869-1989) References Subject Index Citation Index

354 362 374 389

Figures Beginning with chapter 15, the period covered is 18691989, unless otherwise specified. 3.1 3.2 3.3 3.4 3.5 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 8.10 8.11

Profit rates in four industries (1948-1985): r(l) Profit rates in four industries (1948-1985 ): r( 2 ) Profit rat.es in four industries (1948-1985): r( 3 ) Profit rates in nine durable manufacturing industries (1959-1987): r(l) Profit. rates in nine durable manufacturing industries (1959-1987): r( 3 ) Three capitalists and three firms: profit rates Three capitalists and three firms: shares of ownership Stability conditions: r for three values of coefficient e Gravitation: profit rates Rationing: the ratios of inventories Intraindustry competition: prices Intraindustry competition: profit rates Heterogeneous technology: profit rates Limitations to capital mobility: profit rates Credit relations: profit rates Moving equilibria: capital stocks vii

42 42 43 44 44 144 144 145 148 148 151 151 154 155 157 159

viii

Figures

161 8.12 Technical progress: profit rates 8.13 Endogenous wage rate: profit rates 162 8.14 Short-term equilibrium: capacity utilization rates 163 11.1 Manufacturing output, the 1970s 206 11.2 Manufacturing inventories of finished goods, the 1970s 206 11.3 The trade-off between output and inventories, the 1970s 212 11.4 The fluctuations of output and employment in manufacturing industries (1953-1989) 213 11.5 Instability in dimension with three goods: capacity utilization rates 221 13.1 The share of gross profit in GNP (1869-1989) 238 14.1 The postwar decline of the profit rate (19461989) 247 14.2 The World-War-II leap forward of the profit rate (1900-1989) 248 14.3 The historical profile of the profit rate (18691989) 251 14.4 Proxy capacity utilization rate (1869-1989) 251 14.5 Labor cost (1869-1989) 253 14.6 The productivity of capital (1869-1989) 254 14.7 The RRI and the profit. rate (1869-1989) 254 14.8 A pattern in three stages (logistic model) 259 15.1 Historical fluctuations of the profit rate and labor cost 267 15.2 Labor productivity: series and models 274 15.3 Capital-labor ratio: series and models 274 15.4 Labor cost: series and models 275

Figures 15.5 The profit rate: series and models 15.6 Long-term fluctuations of the profit rate and labor cost 16.1 The stock of capital: series and model 16.2 The rate of accumulation 16.3 The number of hours worked: series and model 16.4 The NNP: series and model 17.1 The impact of taxation: pre- and after-tax corporate profitability (1929-1989) 17.2 Profit over fixed capital, and fixed capital, plus inventories and money 17.3 The capital-output, inventories-output, and money-output ratios 17.4 The profit rate on fixed capital and inventories, and on net worth (1952-1989) 17.5 The profit rate in the corporate Manufacturing (1952-1989) 18.1 Wholesale price index (1800-1989) 19.1 The RRI and four profitability spectra 19.2 A measure of heterogeneity, the standard deviations of profitability spectra

IX

275 281 286 286 290 290 296 299 299 302 302 318 340 340

Preface The motivation for devoting a book to the economics of the profit rate, its theory and empirics, originates from our view that the profit rate is crucial to the functioning of advanced capitalist economies. Differentials between industrial profit rates drive the allocation of resources among industries. The profit rate is responsible in large part for the stability of the macroeconomy, i.e., the ability of the system to avoid overheatings, recessions, or depressions and, thus, recurrent bursts of unemployment. The profit rate is further the ultimate criterion in the selection of new techniques of production, and impacts on technological change. It conditions the pace of accumulation and growth. The trend of the profit rate also influences the potential progress of the purchasing power of wage earners. Finally, in relation to this broad variety of effects, the profit rate has a specific historical importance and can provide crucial insights concerning the periodization of capitalism into distinct stages. Obviously, no variable-not even the profit ratecan explain every aspect of the economy: microeconomics, macroeconomics, growth, technological change, and distribution. This study characterizes the profit rate simply as a pivotal variable, and focuses on the relationships between profitability and other mechanisms. At one time, in the 18th and 19th centuries, the profit rate was central to economic theory-in particular, in the works of Adam Smith, David Ricardo, and Karl Marx (the classical economists). Since that time, it has survived only among economists working in the classical and, to some extent, Keynesian traditions. Within mainstream economics, its influence has Xl

Xll

Prefoce

drastically waned. Iudeed, part of the project here is to restore classical economics as sound foundation for economic analysis. But faithfulness to the great forerunners is not our primary motivation. Rather our goal is to build a framework of classical inspiration using the tools of contemporary economics, and to subject the construction to empirical verification. Thus, this book attempts to demonstrate the contemporary relevance of the profit rate with respect to modern economic theory and empirical analysis. The empirical sections of this study focus solely on the US experience. The basic reason for this choice is the relative wealth of data available for this country. But it is equally true that the US played a central role in the world economy over the 120 years considered in this book. This period covers the rise to dominance and, to some extent, the "demotion" of the US economy within the group of advanced economies. The authors are fully aware of the evident limitation of this work. Several aspects of the economy are neglected, as are important segments of the economic literature. In particular, we are deeply convinced tha.t the historical analysis advanced in this book should be related on a world scale, with roots sunk deeper into the past.

We thank Mark Glick for his patient help in the translation of this tezt into English.

PART I THE PROFIT RATE

1. The Economics of the Profit Rate: A Summary In conventional economic terms, the scope of this book might be said to include: microeconomics, macroeconomics, technological change, distribution, fluctuations and growth, and economic history; or for those more technically inclined: long-term equilibrium and its stability, a dynamic model of business-cycle fluctuations, a model of technological change and distribution, with application to the history of the US economy. The political-economy oriented reader will appreciate instead: the classical conception of competition and the formation of prices of production, crisis theory, the rise of the technical composition of capital and the falling profit rate, and the transformation of relations of production under capitalism. All these topics will be touched on in our analysis. One will find contained herein microeconomics, macroeconomics, literary analysis, models, reference to classical economists, econometrics, interpretation of the historical transformation of capitalist relations of production and class patterns, etc. It. is the purpose of this first chapter to demonstrate how these various aspects and methods relate, and how the entire construct hinges on the notion of profitability. This summary is then followed by two brief discussions, in the appendices, concerning the relevance of the profit rate with respect to contemporary capitalism and the classical foundations of this analysis.1 Notes are presented at the end of each chapter. 3

4

The Profi.t Rate

1.1 Competition and resource allocation

• The profi.t rate is a prominent ·rnria.ble in the analysis of competition. One can find, in the works of Smith, Ricardo, and Marx a remarkable analysis of competition, in which the profit rate plays a central role. In the classical perspective, profit rates tend to be equalized among industries in the long term, or to gravitate around a common value. When this occurs, specific prices prevail, called natural prices or prices of production. This property results from the behavior of individual capitalists who seek higher returns for their capital. Whenever profitability differentials appear, a migration of capital is initiated from activities with low profit rates toward more profitable investments. This mechanism, the classicals expected, would eventually correct for these discrepencies. Thus, the profit rate is an important guide in the allocation of resources among industries in the long term. In more mathematical terms, the classical story is equivalent to the analysis of the stability of a long-term equilibrium. The situation in which all profit rates are equalized defines an equilibrium. It is a long-term equilibrium, since capital stocks are modified. Stability analysis is also implied, since the classical economists describe the mechanisms which account for the convergence of the variables from a situation out of equilibrium, i.e., disequilibrium, toward their equilibrium value (or the gravitation of the variables around this equilibrium value). Since it is central to this analysis that the actions of individual capitalists and enterprises (displacement of capital, determination of outputs and prices, etc.) are considered, the point of view is microeconomic analysis. However, such decisions are always made within disequilibrium, and the microeconomics, which we call disequilibrium microeconomics, are not standard fare.

A Summary

5

It is actually possible to demonstrate the consistency of the classical analysis of competition. Three general results can be obtained: (1) Long-term equilibrium exists, (2) Its stability is subject to conditions regarding the behavior of economic agents, and (3) These conditions are easily met. This demonstration can be made in more or less sophisticated models, and is robust when we expand the number of agents, introduce technological change, nonhomothetical growth, money and credit, and some forms of imperfect competition or heterogeneous technologies. However, the notion of "the" classical model of competition, embodying all aspects of this complexity, is only appealing to those uninitiated to the complexities of modeling. In spite of the still abstract character of the analysis, this classical conception of competition, and the central role that it confers on the profit rate, is empirically relevant. In the US economy, average profit rates by industry do indeed tend to gravitate around a common value. (The fact that the profit rates of individual firms may differ, within the same industry, does not contradict this property, and is fully expected within the classical analysis.) Likewise, it is possible to demonstrate that investment responds to profitability differentials. This empirical investigation confirms that the contemporary US economy is still "competitive" in the classical sense, and has not entered a phase of monopoly capitalism.

• The classical conception of competition is different from both the neoclassical and Keynesian perspectives. In the neoclassical analysis2, or in the contemporary formal orthodoxy, the basic paradigm is that of the Walrasian equilibrium, in which equilibrium prices allow for the immediate clearing of markets on the basis of given endowments. This thoroughly unrealistic account of competition within capitalism is alien to the classical perspective, in which equilibrium is reached via the movement of capital (i.e., the modification of

6

The Profit Rate

endowments )-in a long-term process. Equilibrium prices, i.e., prices of production, are independent from the initial distribution of resources. It is also possible to supplement the classical notion of a long-term equilibrium with that. of a short-term equilibrium {on the basis of given capital stocks). Since the changes in fixed capital are slow, the adjustment of supply to demand is realized in the short term by changes in the capacity utilization rates in each industry. Thus, we denote this equilibrium as a short-term equilibrium by quantities. This conception of a short-term equilibrium by quantities is the basis of Keynesian economics. The difficulty with the Keynesian train of thought is that it lacks any real treatment of the long term and, therefore offers only ad hoc and unrealistic extensions of the short term (for example, mark-up pricing at a constant rate) to achieve the long term. • The mechanisms implied in the classical analysis of competition are efficient (as acknowledged by Smith, Ricardo, and Marx). The invisible hand of Smith, or rather the multitude of "greedy" visible hands, do not lead to chaos, but instead guarantee the gravitation of the economy around a situation in which those products which are demanded get produced and then sold at prices which ensure an evenly distributed profit rate among industries, and investment is directed toward industries where more productive capacity is needed. The system has the ability to adapt well to the changing patterns of demand. We denote this property of capitalism stability in proportions, since it concerns the determination of the relative values of the variables among industries, stocks of capital, outputs, and prices. Indeed, investment can be misguided to some extent, inventories may be in excess in some specific segments of the productive system, rationings may be observed at some points of the market, relative prices may fluctuate

A Summary

7

within certain limits. However, capitalists and enterprises correct more or less rapidly for such disequilibria, and it is a general characteristic of capitalism that goods can be purchased and are made available in approximately the right proportions. This is capitalism's strong point.

1.2 lVIacroeconomic (in)stability and the tendential instability thesis • The profi.t rate is also an important determinant of the stability of the macroeconomy. As noted in the previous section, the difficulties concerning stability in capitalism are not reflective of an inability to allocate capital among industries, or to adjust relative outputs and prices, i.e., are not related to what we denoted above as proportions. The difficulties capitalism typically experiences are related to the instability of the general activity and price levels, or what we call instability in dimension. By this expression, we mean that, although balanced growth may prevail for limited periods of time, the macroeconomy is typically on the verge of overheating, recession, or depression. As is well known, recession always seems to be around the corner. It is striking that, in spite of the progress of the social control of macroeconomic stability (in particular, the progress of economic policy), economists and business pundits are always busy scrutinizing the economic horizon, like meteorologists, for indices of future downturns or recoveries. The issue of the comparative amplitude of fluctuations in the general level of activity in the 19th century and after World War II is still controversial. Business-cycle fluctuations are not the unique problem of capitalism, but it is a central issue, and it is where a second important influence of the profit rate may come into play. The propensity of the economy to overheat or to enter into recession (or depression) is conditioned

8

The Profit Rate

by the level of the profit rate. This view was originally part of Marx's analysis of capitalism, and it is tempting to try to ground the theory of business fluctuations in Marx's grand vision of historical tendencies. He thought that low levels of profitability would jeopardize the overall stability of the macroeconomy and could be responsible for crises. The influence of profitability on stability in dimension is related, in our opinion, to the impact of the profit rate on the behavior of enterprises. As a result of lower levels of profitability, more pressure is put on firm liquidity, and this squeeze induces stricter management, i.e., stronger reactions to disequilibrium. In particular, in an environment of low profitability, firms respond to large inventories of unsold commodities (which are the symptoms of the low levels of demand) by diminishing their activity more strongly.3 The modification of behavior in response to the variation of the profit rate is quite rational from the point of view of the in di vi dual firm. However, at the level of the macroeconomy, such reactions can initiate cumulative movements downward (recessions), low output-+low income-+ low demand-+ lower output-+···, or upward (overheatings). This analysis of the effects of the profit rate on macroeconomic stability is not common in economic theory. In the neoclassical, or rather the new-classical, perspective, business fluctuations are conceived of as the manifestation of the optimal reactions to exogenous shocks, and the profit rate never plays a role. Conversely, the profit rate is important in Keynes' analysis-if not in all Keynesian approaches-since the expected profit rate (called marginal efficiency of capital) determines investment and, thus, the level of output. Our interpretation differs from Keynesian analysis in, at least, two respects: the profit rate impacts on firm supply behavior instead of demand, and affects the stability of the level of activity, instead of the level itself.

A Summary

9

• A growing instability of the macroeconomy is created by the progress of private management, and then checked by the subsequent development of the institutional social control of stability. The pressure experienced by firm managers during the recurrent periods of actual decline in the profit rate, as well as the constant incentive to improve management, is responsible for a paradoxical bias toward increased instability in the macroeconomy. This tendency is counteracted by the growing efficiency of the institutions responsible for the control of macroeconomic stability: economic policy, and regulations and laws. We denote as the tendential instability thesis this vision of the simultaneous progress of destabilizing decentralized forces and counteracting social stabilizing devices. Periods of actual macroecomic instability correspond to the lags in the implementation of the new social control of stability following the rise of destabilizing forces. The evolution of the institutions in charge of the control of stability responds to the manifestations of instability, but with a lag. This explains why the economy typically remains in a situation close to the limit between stability and instability, which we call the stability frontier. Note that this view provides a privileged place to the complementary character of the progress of individual and social "management."

1.3 Technology, distribution, and accumulation • The profit rate is a prominent variable in the determination of the profile of technological change and the progress of wages. Wages and technology allow for the calculation of the profit rate. Conversely, the profit rate also impacts on technology and wages: 1. Comparative profitability is the primary criterion de-

termining the choice and survival of new techniques of

10

Tl1e Profi.t Rate

production. Given wage levels and the prices of other inputs, the techniques that yield the larger profit rates are likely to be selected. 2. There is a feedback effect from the profit rate to wages. Large (and rising) profit rates create conditions that allow wages to rise faster, and low (and declining) profit rates result in the slower growth of wages. Actually, all of these variables are part of a complex network of reciprocal interactions. The profit rate is crucial in conditioning technological change; but it is affected by the rise of wages, which, in turn, impacts on technology; technological change affects the profit rate, which further relaxes or reenforces firm resistance to the advance of wages, etc. The profit rate plays a key role in these interactions. It is not simply a ratio that one may or may not. recover from the dynamics of the system. In this, it considerably differs from the profit share which does not directly affect the behavior of economic agents. The outcome of these mechanisms as it can be traced in historical data for the US economy since the Civil War is twofold: 1. They produce a declining profit rate, a rising la-

bor productivity, as well as rising capital-labor and capital-output ratios, in conformity with what can be called a historical profile a la Marx. 2. Whenever, the profit rate plunges to unusually low values (actually twice in the period considered), the overall evolution of the economy is slowed. One should notice that this analysis focuses less on labor productivity than is standard in the literature, and more on the profit rate. Wages are not pegged (directly or indirectly) to labor productivity, and the declining profit rate in the last several decades is not. explained by the (labor) productivity slowdown, but rather we will assert that the reverse is the case. As we will see, this analytical scheme accounts quite

A Summary

11

well for the trends observed during most of the 121 years considered here. During the intermediate period which runs from the early 20th century to the 1950s, a strong acceleration of technical progress was superimposed on the above mechanisms. It allowed for an exceptionally rapid growth oflabor productivity, whereas the capitallabor ratio was restrained to slower rates of growth and the capital-output ratio declined strongly. These movements combined in an upward trend of the profit rate, which, in turn, made a faster increase of wages possible. Thus, the historical fluctuation of the profit rate, downward/ upward/ downward, defines a broad periodization into three stages: late 19th century/ early 20th century/ second half of the 20th century. This long intermission in the evolution of technology and distribution caused much concern among Marxist economists. In the 1960s, it became clear that it was important to account for the large profitability levels reached after World War II. The tendency for the profit rate to fall was said to be characteristic of 19th century competitive capitalism, and the increased profit rate in the 20th century was linked to the existence of monopoly capitalism-as if a transformation of competition could account for the movements of the average profit rate. The empirical evidence for a new decline in the third stage is now well accepted, and this book emphasizes the strong similarity between the first and third stages. In spite of its duration, the central episode is treated as a transitory "interruption" in a basic historical tendency.

• The historical profile of the profit rate in three stages was also reflected in the pace of accumulation. The slackening in the growth rate of fixed capital in the early 20th century is linked to the low levels of the profit rate. However, deficient profitability only explains a part of this phenomenon, which primarily mirrors the sharp reduction in the rate of accumulation (the fraction of profit devoted to accumulation) around World War I. Since then, the rate of accumulation has

12

The Profit Rate

been maintained and the growth of the capital stock directly reflects the levels of the profit rate.4 Thus, accumulation surged again after World War II, until the "recent" slowdown related to the new plunge of the profit rate. 1.4 History

• The profit rate is a prominent variable in the peri.odization of capitalism. The distinction between several periods, phases, or stages, in the history of capitalism can be derived from various categories of phenomena, such as competition, technology, dist.ribution, stability, institutions, etc. There is nothing puzzling in this variety of competing criteria. It echoes, quite naturally, the degree of complexity of the mechanisms under consideration. However, because of the central role that it plays in the historical dynamics of capitalism-with respect to technology and distribution, as well as macroeconomic stability and institutions-the profit rate is a particularly promising candidate. For this reason, we will use the periodization in three stages corresponding to the historical fluctuation of the profit rate, introduced in the previous section, to delineate three stages in the evolution of US capitalism since the Civil War: late 19th century/ early 20th century/ second half of the 20th century, or first period a la Marx I intermediate period/ second period a la Marx.s We do not contend that the Civil War corresponds to any specific break in this evolution. 1869 is simply the first year in our series, and it is quite possible that the trends observed during our first period began earlier. Starting with the Civil War, the last decades of the 19th century up to the early 20th century can be characterized as a period a la Marx. In the late 19th century, in conjunction with the low levels of profitability, a strong instability was manifested, and the system seemed to

A Summary

13

reach a deadend. It recovered from this situation, but at the cost of an important modification in the relations of production, the rise of managerial and clerical personnel, and the retreat of many traditional capitalists to the finance sector. Thus, the business staff enjoyed a greater autonomy in the control of management and technology (of which some aspects have been portrayed as Taylorism). This transformation was paralleled by the gradual emergence of new institutions related to the social control of macroeconomic stability (in particular, the substitution of new centralized procedures for the issuance of money for the old Gold Standard). As a result of this "managerial revolution," rapid technical progress without the typical increase in the capital-output ratio occurred. Rising profitability made possible an unusual rise in real wages, and allowed for a new form of political compromise. But there were also a number of drawbacks to these benefits. First, the sweeping acceleration of technological change resulted in a greater heterogeneity in technology among firms. Exceptionally large fractions of the capital stock became obsolete and were devalued. Second, the withdrawal of capitalists from the productive sector and their retreat into finance led to the erection of a fragile financial edifice, connected to the stock market and a new banking system.6 This heterogeneity of technology, coupled with the emergence of this tremendous financial superstructure, added considerable fragility to the economy, and this fragility was not offset by a mature economic policy establishment. These trends finally dramatically culminated in the Great Depression. As is well known, the Great Depression and World War II took care of the second facet of the metamorphoses already initiated in the early 20th century, with an increasing role of centralized institutions and state intervention. The US economy emerged from the war with high profit rates, experience in economic stabilization, and a commitment to the control of the macroeconomy. In the third period, after World War II, the con-

The Profit Rate

14

clitions remained favorable until the late 1960s, when the reduction of the profit rate was again directly felt by enterprises. This reemergence of the old trend was manifested in a "crisis," which remained latent as a result of the improved control of stability. This crisis was also manifested, however, in a surge of inflation, a new accumulation of business fluctuations, and a chronic inability to balance the budget, as the state was forced to relax the tax burden it had earlier imposed on firms. An important feature of capitalist economies, related to the existence of disequilibrium (short-term market disequilibria, small and large crises, etc.), is that they are, to a large extent, controlled ex post. It is the evidence of disequilibrium which provokes reactions, in the short and long terms, on the part of firms or monetary authorities. Firms respond to market disequilibria by modifying their outputs and prices, or capitalists can react to profitability differentials by moving their investments. The prolonged experience of low profit rates induces the progress of management, the transformation of technology, and reduces the growth of real wages. It is the accumulation of recessions and unemployment which stimulates the transformations of the institutional framework responsible for the social control of stability. While the system may eventually be brought under control-in particular with respect to profitability levels -the constant adjustment is performed at the price of recurrent malfunctionings and particularly intense episodes of tension and crisis.

NOTES 1.

2.

Obviously, this study borrows considerably from earlier research. One ean cite, in particular, two papers in which a synthesis had been attempted: Dumenil G., Levy D. (1991(d) and 1992(a)). By neoclassical analysis, we refer to a school of thought (often, more or less questionably, identified with "marginal-

A Summary

3. 4. 5.

6.

15

ism"), and by Walrasian, we mean a set of models of general equilibrium with immediate market clearing by prices. The neoclassical perspective is broader, and less strictly defined, than Walrasian models. It builds on Walrasian foundations, with a clear "free-market" stand. The same point. of view of perfect price flexibility has been extended to macroeconomics by "new classicals." A new formal (mathematical) orthodoxy (which also includes "new Keynesians"), in which agents optimize with rational expectations, now dominates the mainstream. Of course, symmetrical reactions are developed for depleted inventories, or for large profit rates. The capacity utilization rate is also an important determinant of accumulation. Competing periodizations can be found in other contemporary heterodox approaches to the evolution of capitalism, such as Mandel E. (1980), the Social Structure of Accumulation in the US (Gordon D. 1980 or Gordon D., Edwards R., Reich M 1982), or the Regulation School in France (Aglietta M. 1979 or Boyer R. 1989). The movement of the rate ofreturn on investment rose sharply in the 1920s, and the surge of the stock market was not totally deprived of real foundations (cf. section 19.2).

16

The Profit Rate

APPENDICES 1.Al Is the profit rate irrelevant or obsolete? The emphasis placed in this book on the role played by the profit rate is not generally accepted. In the neoclassical or new-classical paradigm, final consumers, with their intertemporal utility function, are the crucial agents. The treatment of firm behavior tends to replicate that of final consumers, and deprives enterprises of their real-life status, as autonomous institutions. The profi.t rate cannot have an important place in this neoclassical universe. Within the Keynesian train of thought, the central issue is the level of demand. Firms simply respond to demand signals. Supply is fixed at the level of demand, and investment, in the accelerator model, follows primarily demand, and not profitability signals. Even among Marxist economists, the full importance of the profit rate is not always acknowledged. The role of the profit rate in the analysis of competition and the allocation of capital is sometimes ignored; the impact of the profit rate on stability is not understood, and the origin of crises is instead detected in sectorial maladjustments or deficient demand; the tendency for the profit rate to fall is often abandoned because of theoretical or empirical objections. A very common contention among heterodox economists is that the profit rate used to be a crucial variable, in an earlier "competitive" stage of capitalism, but that the classical analysis of competition has lost its explanatory power vis-a-vis contemporary "monopoly capitalism." A first version of this analysis is still compatible with the view that firms maximize their profit. Because of the monopolistic character of competition, firms fix prices by marking up costs. Increasing barriers to capital mobility have been erected and prices no longer gravitate around prices of production. In our opinion, this vision lays too much emphasis on short-term mechanisms, in a Keynesian fashion. Obstacles to capital mobility are never permanent, and monopolies eventually fall. Long-term adjustments are critical and condition the short term. Disequilibria in the short term are maintained between manageable limits, thanks to these long-term mechanisms. It is presumably true that the classical school paid excessive attention to the long term, and that the Keynesian revolution was useful in this respect, but the problem is actually to "articulate" short- and long-term analyses, and not to pick one approach at the expense of the other.

A Summary

17

A second version pushes the analysis even one step furtl1er. In this view, firms or capitalists no longer maximize their profit rate. They maximize their growth rate or attempt to increase their market share. This view is reenforced by the observation that actual power within firms has shifted from capitalist owners toward salaried managers. Within a given industry, firms must compete for outlets. However, growth implies investment and financing. Growth at any cost, independently of profitability levels, is certainly not tl1e ultimate objective of firms in the long term. Capital is still a limited resource, and the various channels by which it can be collected all depend on expected or realized profit rates. The comparison of various opportunities is always crucial in the decision to invest. The denial of the function of the profit rate in the long term simply o\.·erlooks the capitalist nature of our economies, and ignores the power of those who have control over capital.

1.A2 Tbe classical legacy and beyond The brief summary in this chapter of the contenis of the book raises the issue of the degree of classical inspiration of this anal.vsis. How faithful are we to this perspective? Do we restore or develop the analysis of Smith, Ricardo, and Marx? Actually, our intent is to use the classical legacy only as a point of departure in exploring new territories. It is certainly not possible to simply set aside a century of economic theory to build on purely classical grounds, but our project is based on a quite specific interpretation of the history of economic thought that points to the necessity of a restoration. In the pre- Walrasian stages of the development of economic theory, a classical approach had reached its pinnacle of maturity in the works of Smith and Ricardo. This perspective was later preserved and, in some important respects, transformed by Marx. Briefly, four basic paradigms can be found in the work of these economic theorists: 1. A labor theory of value. Labor is seen as the substance of value.

This concept of value differs from that of prices, but the clearcut distinction between value and price is more or less rigorous depending on the economist considered. 2. Competition, prices of production, and the mobility of capital. As a result of the migration of capitals in search of maximum

18

The Profit Rate

profitability, profit :rates tend to be equalized. This analysis is very similar in Smith, Ricardo, and Marx. 3. Crisis. Although the modern business cycle appeared only after 1820 in England, Ricardo already displayed some interest in these states of distress, in his words, that the economy periodically confronted. Later the issue of crisis became crucial in Marx's analysis of the working of capitalism, and was clearly disconnected from the formation of prices of production. 4. Historical dynamics. Although they provide different interpretations for their existence, the three economists point to a number of historical tendencies, such as t11e tendency for the rate of profit to fall. They are deeply concerned with history and the metamorphoses of capitalism. The classical construct is still deficient in many respects, but it provides a very promising basis on which to develop economic theory. Unfortunately, the theoretical difficulties of the post-Ricardian school which culminated in the work of Alfred Marshall left a clear field for the neoclassical (or marginalist) revolution. Later, the inability of this new current of thought to deal with the actual problems of capitalism, in particular, its inherent instability in dimension, made necessary a second revolution, now named after John Maynard Keynes. However, this new development never threatened the foundations of Walrasian economics, to which it is now combined in various syntheses. In our opinion, the problem today is not to recombine Walrasian and Keynesian analyses, but to realize that the abandonment of classical economics was, in fact, detrimental to the advance of economic knowledge. A powerful and coherent basis for a new framework exists within this analysis, taking advantage of the modern tools and methods of economics. The outline of this study directly mirrors its classical inspiration. It draws on the three later paradigms above, competition, crisis, and tendencies and it, finally, tries to provide a historical synthesis. Onl.v the first paradigm, value theory, is not considered in this study, for :reasons which will be discussed in due course.

2. Definitions and Measures of the Profit Rate It could be argued that the title of this book implied that the notion of the profit rate has a precise definition. The same might be argued for the first chapter above, where the profit rate was related to resource allocation, macroeconomic stability, technological change and distribution, as well as history at a more general level. In each case, a uniquely defined term was supposed to account for a very large variety of phenomena. Unfortunately, the situation is more complex, and it is not possible to add precision to this broad synthesis by referring to a single definition. Instead, profitability must be approached in different manners, depending on the exact problem considered. Once an appropriate definition of the profit rate has been choosen, the empirical section of the analysis raises a number of new difficulties: which sources, which series, what period and unit of analysis, etc ? The difficulty in finding reliable data obviously increases as we go back in time. We believe, however, that it is important to resort to an empirical foundation to formulate hypotheses concerning the historical evolution of the economy, instead of relying too heavily upon arbitrary guess work. It is the purpose of this chapter to consider many of these issues. The discussion of the definition of the profit rate is followed by a brief introduction to available data sources. We then turn to a more technical discussion concerning the exact contours of the two aggregates, 19

20

The Profit Rate

profit and capital. The relationship of this discussion and the previous chapter as well as the rest of this study is considered in the last section, which is devoted to the choice of definitions in relation to specific problems.

2.1 The profit rate and related notions A profit rate is a ratio of a measure of profit to a measure of capital, profit/ capital: 1. Profit is a flow which can be expressed as the difference

of two other flows: output- costs. 2. Capital is a stock, i.e., a sum of money which has been invested in a certain line. A specific vision of the business firm lies at the basis of this notion of profit rate. A certain quantity of money has been advanced-and this implies that it is tied up in a particular activity and is no longer available for other uses-in order to generate a flow of returns. Once current expenses have been deducted from this flow, the remainder, profit, appears as the remuneration to the original advance, capital. It is, therefore, quite natural to compute the ratio of profit to capital, to measure the efficiency of the enterprise. A capitalist economy is a social system in which production is financed by these advances of capital invested in firms, whose activity is conditioned by the size of the advance. This tight relationship between the notion and the nature of the economy explains the crucial importance of the variable. The denial of this role can often be understood as an attempt to conceal the true nature of the mode of production. The profit rate is important in a capitalist economy, because it directly measures the performance of capital as such. Profit can be assessed in reference to variables other than capital. An alternative ratio is the share of profit. It is obtained by dividing profit by total income. It is a ratio between two flows, and reflects a straightforward

Definitions and Measures

21

measure of distribution, but it does not mirror directly the ability of capital to make profit. Of course, if the share of profit increases, whereas total income and capital remain constant, the profit rate will also be larger. It is also true that the profit share is easier to measure than the profit rate, since this measurement does not require a measure of capital, but this does not justify the confusion of the two notions that is frequent in the literature. A profit rate also differs from a profit margin, which is the ratio of profit to costs. This ratio is also quite meaningful in several respects. It relates profit to the price of the inputs (raw materials, energy, labor and, possibly, depreciation of fixed capital, etc.) required for the production and commercialization of the good, but it does not measure the ability of the stock of capital to yield profit. The same remarks can be made as in the case of the share of profit, which is sometimes used as a kind of macroeconomic "profit margin." A profit rate is also quite distinct from a rate of interest in the sense that the yield and return on capital are fixed by contract in the latter case. Once the decision to lend has been made, the lender is no longer in charge of the operations for which the loan has been made. The rate of interest can be described as a form of "contractual" profit rate. There are several problems related to the units of measurement in the definition of the profit rate: 1. The advance is made in prices, and profit is realized in price terms. The profit rate must be measured with aggregates expressed in this unit. 2. Capital must be evaluated at its current cost, i.e., using the prevailing replacement prices (not in constant dollars, nor at its historical cost, i.e., the price at which the various components of capital have been purchased years ago). Note finally that the profit rate discussed to this point is an accounting profit rate on the stock of capital. This

22

The Pro:fi.t Rate

expression refers to three specific features of this measure of profitability: 1. It is the profitability of the stock of capital outstanding

which is measured. 2. The profit rate is defined for a given time span, one year, for example. 3. The depreciation of fixed capital is estimated by an accounting schedule.I Another view of profitability relates the advance, when it is made, to the future fl.ow of profit that it will generate over its entire life. This measure of profitability is known as the rate of return on investment. It is the discount rate which equalizes the present value of the fl.ow of returns to the value of investment. This rate is considered by many economists as the most relevant economic approach to profitability.2 This measure is also interesting since it takes account of the temporal element implied in investment. It is, however, more difficult to measure than the accounting profit rate. 2.2 Sources

In order to compute a profit rate, regardless of the definition selected, one must rely on imperfect data. Economists like to complain about the lack of appropriate data (in particular concerning the capital stock). It must be acknowledged here, however, that the available set of data for the US economy is remarkable. Beginning in 1929, it is possible to determine measures of the profit rates, abstracting from the monetary and financial components of capital, on the basis of a very coherent set of data-particularly in comparison to other countries. A very broad set of data is available from the Bureau of Economic Analysis (BEA). It is composed of two main blocks: National Income and Product Accounts

Definitions and Measures

23

(NIPA) and Wealth data. NIPA provides estimates of the main flows necessary to compute the numerator of the profit rate (product, labor compensation, taxes, etc.) and inventories. Wealth data provide estimates of capital stocks and depreciations. NIPA 's basic series begin in 1929, and the capital series are available from 1925. BEA series concerning capital are restricted to fixed capital and inventories, and exclude all monetary components of capital. However, for the period following World War II, the Federal Reserve publishes detailed monetary and financial accounts known as Flow of Funds and Balance Sheet for the US Economy. On this basis, the monetary components of capital can be added to real components. Note that, in our calculations, all series come from BEA, for the period 1929-1989. The sometimes puzzling profiles revealed for these years only reflect BEA 's evaluations. Needless to say that the difficulties multiply as we go back in time, and the estimates become less reliable. Prior to 1929, it is necessary to resort to historical studies. Several such authoritative studies exist for the US economy. We used, in particular: Balke N .S., Gordon R.G. 1989 for GNP, Goldsmith R.W. 1952 for the capital stock, Kendrick J.W. 1961 for employment, and Lebergott S. 1964 for labor compensation. Data obtained from these studies must be combined together with those described above, and some work is required to obtain a coherent set of data (cf. Dumenil G., Levy D. 1991 (a)). The observation of strong, sometimes unexpected, regularities among series derived from quite distinct sources lends confidence to the set of very longterm data used in this study, which begins as early as 1869, and covers a period of 121 years. Other sources are also available, such as data directly derived from private accounting (used for financial analysis). It is also possible to resort to data collected in

24

The Pro:lit Rate

relation to taxation, and published by the Internal Revenue Service. These sources can be helpful, in particular, for the computation of industrial profit rates, but capital stocks are evaluated at the price at which they have been acquired (historical cost), and this limits considerably their usefulness. 2.3 Technical problems

As can be easily imagined a number of difficulties are faced in the practical computation of profit rates. Once the three aggregates, capital, output, and costs, have been determined, it is possible to compute the profit rate. But a number of alternative definitions of these variables can be chosen and, consequently, a broad variety of profit rates can be determined. There are several definitions of output in national accounting. The two basic measures are Gross National Product (GNP) and Net National Product (NNP). In the NNP, a measure of the depreciation of fixed capital is subtracted, and this is the most adequate deli.nit.ion for the computation of the profit rate.3 Since costs corresponding to goods and services purchased from other enterprises are already subtracted in the determination of the product to avoid double counting, all other costs are forms of income. For example, the cost of labor is equal to wages plus employee and enterprise contributions to various programs (health, retirement, etc.). This aggregate is known as total compensation. A problem arises as a result of the existence of self-employed persons. The nature of their remuneration is ambiguous, and not. easy to impute between profit and labor income. This problem is quantitatively important because of the historical reduction of the number of the self-employed, in relation to the rise of corporations. It is necessary to correct for this increasing "salarisation."4 Once the cost of labor has been subtracted from

Definitions and Measures

25

the product, the difference provides a first measure of profit. It is clear, however, that this measure is very broad, and does not reflect the final income of firms. A number of other components should also be subtracted. These costs fall into two categories: interests and taxes. One may, or may not, subtract from profit the difference between interests paid to other agents and earned by firms. Two categories of taxes should be considered: indirect business taxes and corporate profit taxes. Again, one may, or may not, subtract these taxes. A specific difficulty concerns profit taxes, since these taxes a.re paid only by the corporate sector. The tax paid by the noncorporate sector is the personal tax. For this reason the determination of a complete after-tax profit is only possible for the corporate sector. Profit realized by corporations after the payment of all taxes can again be subject to a further deduction, the payment of dividends to shareholders. Important difficulties are also implied in the estimation of capital. Capital is composed of several component~: land, fixed capital, inventories, and financial assets. The details need not be discussed here, and we will limit the analysis to the three latter items, beginning with fixed capital. A number of options are available for the determination of the stock of fixed capital, the denominator of the profit rate. It can be computed gross or net of depreciation. Important alternatives are also at issue concerning the exact components of fixed capital to be considered. Three kinds of capital stocks are distinguished in the series: structures, equipment, and residential capital. A specific problem is met concerning residential capital, which may be included in the capital stock or may not. In some cases the distinction between the structures and residential capital is rather arbitrary, as is the case for Agriculture. The evaluation of the capital stock from the BEA is based on the perpetual inventory method and, for benchmark years, checked against the Census. With

26

The Profit Rate

this method, the gross stock of fixed capital for a given year is determined as the outcome of two opposite fl.ows. The infl.ow corresponds to gross investments and the outfl.ow to discards: Investment Discards Gross capital If the series of investments and discards are known, it is possible to derive a series for the capital stock by summing over all vintages. A series of investments is determined from historical evidence. Discards are computed on the basis of discard schedules, named after Robley Winfrey, who developed them. These schedules indicate for each category of capital good the time profile of its retirement. A similar method is applied to compute the net stock of fixed capital, but a depreciation schedule is used instead of a discard schedule. These procedures are based on average economic conditions. It is obvious, however, that actual discards are influenced by the macroeconomy. This problem is significant, for example, in the assessment of the effects of the Great Depression on the capital stock. Under such exceptional circumstances, some fractions of the capital stock may yield negative profit, even if only variable costs are considered, and will be discarded. Since the discard schedules do not account for such economic discards, a bias may exist. These difficulties could lead, for example, to an overvaluation of the capital stock in the wake of the depression, which would disappear only gradually in the subsequent decades. Another difficulty in the estimation of fixed capital is associated with the influence of the state in investment during World War II (and after the war, up to the 1960s, to lesser extents). A significant fraction of the capital stock of the productive sector of the economy was financed by the state during the war, leased, and eventually sold after the war to the private sector, at

Definitions and Measures

27

a very low price. (In 1943, this kind of investment in the corporate sector represented twice the private investment in equipment and structures.) This is called Government Owned Privately Operated capital. These fractions of the capital stock have always been included in the estimations of fixed capital in our computations. Inventories of raw materials, goods in process, and finished goods are also part of capital. They may be included or excluded from the denominator of the profit rate ( assuw.ing that. the series are available). Financial assets define a last component of capital. This elusive aggregate is made up of various accounts held by firms within financial institutions, securities, and credits to other agents. A new difficulty is faced here because of the reciprocal character of many of these assets. For example, a major item is trade credits which accounts for credits provided by firms to each other. When taking account of the productive system on a global level, should we consolidate, and cancel these credits? The same problem is posed for securities, or deposits, when nonfinancial and financial enterprises are aggregated. Total capital can also be approached from the liability side of the balance sheet. It is possible to define capital as net worth (or shareholders' equity, for the corporate sector). There is an accounting and a market valueat least for one fraction-of this measure of capital. The accounting estimate is obtained by subtracting all debts from total assets. The market value of equity designates the evaluation of shares by the stock market. There is also a market value of debt, the price of the debt. in the capital market. Last, the computation of a profit rate necessarily refers to a given unit of analysis: total business, private sector, corporate sector, sole proprietors and partners, or specific industries such as Manufacturing or Nonfarm Nonfinancial, or other possible breakdowns.5

28

The Profit Rate

2.4 The appropriate definition? There is a fundamental commonality in all the definitions of the profit rate, that makes it relevant to refer to a single concept. However, the notion of a single profit rate, "the" profit rate, appropriate in the treatment of any issue, is misguided. Different definitions must be used depending on the specific investigation. This requirement of using various definitions echoes the broad variety of fields in which the profit rate plays a role. As stated in chapter 1, we distinguish between four such basic fields: capital allocation, business-cycle fluctuations, technology and distribution, and historical trends. Below, we will use this division to illustrate the correspondence between each category of problem and a particular definition, or group of definitions. A first issue is that of resource allocation in the long term. The profit rate is a prominent guide in the allocation of capital among industries and firms. Capitalists respond to profitability differentials by investing more in industries or firms where profitability is comparatively higher. In a similar manner, within multiproduct firms, productive capacity is increased in lines where the profit rate is larger. The problem here is to determine to which profit rates capitalists (or firm managers) are sensitive. It is rather obvious, for example, that profit should be measured after indirect business taxes, or that a measure of capital larger than fixed capital should be used. Indirect business taxes must be paid in any instance, and a difference of profitability before taxes would be misleading. In a similar manner, inventories must be financed, and any assessmeut of profitability which ignores this reouirement is biased. Other choices are less obvious.6 A second issue, where the impact of profitability is important is macroeconomic stability. The influence of the profit rate on the stability of the macroeconomy

De:fi.nitions and Afeasures

29

flows through firm hehavior. Low profit rates induce "tighter" management, for example, stronger reactions to stockpiling. The definition of the profit rate to be considered in this investigation must be closely linked to the bottom line of firms, and directly related to cashflow mechanisms. Profit should be measured after all taxes. It is not obvious, however, whether depreciation should be deducted or not. In a similar manner, a broad definition of capital should be selected, including inventories and some financial assets. The problem is quite different concerning the historical analysis of technological change. The comparison of various technologies must basically be performed using a profit rate definition which combines a broad definition of profit, and a narrow definition of capital. Profit is measured as product minus labor income, and capital is limited to fixed capital. Abstracting from prices, and with the following notation: Y K L II W PK PL w 7r

Output Capital stock Employment Profit: Y - W Total compensation: Lw Capital productivity: output/ capital = Y / K Labor productivity: output/ labor= Y / L Unit real wage rate Share of profit: II /Y

the profit rate can be written: r

= KII = Y-W K

= PK

(

w) =

1 - PL

PK7r

(2.1)

Note that it is sufficient to know the productivity of labor, the productivity of capital, and the wage rate to determine the profit rate in this definition. These various definitions of the profit rate are obviously linked. Definitions closer to the functioning of

The Pro:B.t Rate

30

firms can be derived from the above "technological" definition, subtracting taxes from profit, or adding some components to fixed capital. In this sense, this technological measure determines the other ratios. There is undoubtedly some meaning in the derivation of the historical profile of the profit rate, which begins with technology and wages, accounts progressively for the impact of institutions, such as the financial system or the state, includes, at some point, inventories and financial assets and, thus, moves from a rather simple definition to a more concrete framework, closer to the actual behaYior of firms. Two conclusions follow from this brief discussion. First, the specification of the nature of the problem investigated helps determine the proper profit rate definition. Second, ambiguity remains in some respects, which may, or may not, matter empirically. Thus, the choice of a profit rate, even in respect of a rather well defined problem, remains part of the research program.

NOTES 1.

2. 3.

4.

One must distinguish between depreciation schedules used by firms and BEA. The former is defined on the basis of the regulations of the Internal Revenue Service, and the latter is based on BEA's estimates of the service lives of capitals. Keynes' marginal efficiency of capital is an expected rate of return on investment. In the definition of the product to be used in the computation of the profit rate, a number of choices must be made concerning dubious components, for example, rental income of persons and, in particular, imputed rents to homeowners. A simple way to perform this correction is to assume that the income of self-employed persons is made up of two components, a compensation equal to that of a similar category of personnel and profit for the remaining fraction. Practically, this can be done by determining the total income of labor as

Definitions and Measures

5.

6.

31

the product of the total number of persons, self-employed and employees, by the average total compensation of an employee. The decomposition into various industries poses a complicated problem, since firms are often involved in a broad set of activities related to different industries. In the investigation of capital allocation, should we deduct corporate profit taxes from profit? If taxation is uniform, i.e., if taxes are proportional to profits, the option will not make any difference, but this neutrality is not absolute. A further complication is that all firms are not corporations, and that taxation differs. Similar problems exist concerning the financial components of the balance sheet, on the asset or liability sides. Can we extend the definition of capital to include all financial assets? Consider, for example, trade credits. Some industries are the customers of other industries and may benefit, in this respect, from trade credits. Through such practices, some industries contribute to the financing of others. These relationships are general, but do not necessarily cancel out for a given industry. For example, manufacturing industries sell more to Trade, than the opposite. Consider now liabilities, does the analysis of capital mobility concern net worth or net worth plus some debts? Are the various channels of financing (self-financing, stock market, borrowings) neutral? The answers are again not obvious.

PART II COMPETITION AND PRICES OF PRODUCTION

3. Prices of Production This second part of the book is devoted to the classical analysis of competition and prices of production. In the definition ofthis project, we obviously assume that there are serious grounds to refer to a classical school and, more specifically, a classical analysis of competition. It is always difficult, however, to define the exact boundaries among various schools of thought within economics. Keynes himself is one approach, and Keynesians, another. Even among Keynesians, further distinctions must be made among various subcategories, such as neo- or post-Keynesians. The common reference to a neoclassical train of thought is also quite ambiguous. It may concern Marshallian economics, the neoclassical synthesis, as well as "new-classical" economics, which define some extreme form of neoclassical macroeconomics-and even the definitions to be given to each of these terms are not straightforward. There is also some ambiguity in the definition of the classical perspective that we adopt. For clarity, we like to mention explicitly the trinity Smith, Ricardo, and Marx. The classification of the three economists under the same label is also controversial in some respects because of very fundamental theoretical and political differences,1 but, concerning competition and prices of productioD;, Smith, Ricardo, and Marx clearly shared common views. It is also clear that it is difficult, adding progressively more and more precision to the classical analysis, not to transgress its boundaries. The line between what can still be considered as some form of "exegesis," on the 35

36

Competition

one hand, and actual developments, on the other hand, is marked in the outline of this study by the separation between parts II and III. The second part remains close to the work of the three economists: from the analysis of prices of production, in the present chapter, and its formalization as a long-term equilibrium, in the next chapter, to the investigation of the stability of this equilibrium in the following two chapters. The third part clearly oversteps the limits of the classical terrain traversed in part II. The main purpose of the present chapter is to briefly outline the theory of prices of production and to illustrate its empirical relevance. A section is devoted to nonreproducible resources, returns, and rent-an analysis which supplements that of prices of production. A few remarks concerning the famous "transformation" of values into prices of production are presented in an appendix.

3.1 Classical long-term equilibrium As is well known, Smith, Ricardo, and Marx shared the same notion of natural prices, or prices of production, as distinguished from market prices. These prices ensure equal profit rates in the various industries: [...] suppose that all commodities are at their natural price, and consequently that the profits of capital in all employments are exactly at the same rate [...] (Ricardo D. 1817, Ch. 4, p. 50)

It is, perhaps, less well known that specific sets of outputs are associated with prices of production. For example, in Smith, these outputs are called effectual demands. Effectual demand is defined as: [...] the demand of those who are willing to pay the natural price of the commodity [...] (Smith A. 1776, Ch. 7, p. 49)

In Marx, while the terminology is different, the concept is the same. These outputs are called social needs:

Prices of Production

37

[...] if this market price is to correspond to the market value, and not diverge from it, either by rising above or falling below, then the pressures that the various sellers exert on one another must be strong enough to put on the market the quantity of commodities that is required to fulfil the social need, i.e. the quantity for which the society is able to pay the market value. (Marx K. 1894, Ch. 10, p. 281)

(Note that Marx considers here only market values; he later extends his point to prices of production.) There is a direct relationship between the two properties, equal profit rates and given proportions of outputs. When prices of production prevail, the rates of profit are equalized and, thus, capital is not moving from one activity to another; the proportions of outputs are determined. Although there is always some reluctance within classical economics to use the terms equilibrium or general equilibrium, this situation should be denoted as an equilibrium.2 The time frame involved here is clearly the long term in the conventional sense of the term, since capital investments are made. (A short-term horizon is based on the assumption of given capital stocks.) This long-term horizon is not that of historical tendencies, or very long term, and technology is considered as given, or changing at a slow pace. Classical economists assume tacitly that the target around which the economy gravitates may be drifting over time, because of distributional and technological changes (or the modification of tastes), but comparatively slowly, and it is for this reason that they abstract from these variations in their analysis of competition. Only Marx explicitly treats the relationship between the two time frames, and emphasizes the heteregeneous character of technology within each industry, and its constant alteration. Abstracting from these movements, the equilibrium is a homothetical balanced growth path. Another important but implicit assumption is that the macroeconomy is analysed under "normal" conditions.

38

Competition

The discussion in the chapters devoted to prices of production abstracts from business fluctuations and crises. The economy is supposed to gravitate normally along a kind of equilibrium. The mechanisms described are precisely those which allow for this gravitation. This viewpoint does not deny that other circumstances may prevail, but simply abstracts from them. 3.2 N onreproducible resources, returns, and rent

One of the basic characters of the classical analysis is the strict distinction it makes between nonreproducible resources, such as land, and reproducible resources. The analysis of these two categories of resources is the object of two quite distinct theories, the theory of rents, on the one hand, and prices of production, on the other. It is, therefore, important to clearly contrast and articulate these two aspects of the classical analysis. As is well known, rent on land-in its crudest form -results from the appropriation of the extra profit which accrues originally to the capitalist farmer by the landlord, because of the relative fertility of the soil. The price of the product must be fixed at a level sufficient to provide the farmer investing his capital on the less fertile land with the average profit rate. If such prices prevailed, farmers using more fertile lands would appropriate profits larger than normal in relation to their capital. The landlord can raise the rent up to the point where the comparative advantage of his land is offset. Fundamental differences are implied in this distinction between rent and prices of production. Consider first prices of production (for reproducible resources): 1. The central notion is an equalized profit rate. 2. Returns, assessed at the level of the industry, are constant, because of the possibility of increasing the number of identical units of production in the long

Prices of Production

39

term. 3. Initial endowments (in raw materials and fixed capital) affect market prices, but not prices of productionthe values of prices of production are independent from these endowments. 4. Prices of production are not functionally determined by the quantities produced. Consider next the theory of rent (for nonreproducible resources): 1. Rents are not equalized. The notion of equalizatior1 is antagonistic to the theory ofrent. Unequal rents allow for the equalization of profit rates among capitalists. 2. It is consistent with the theory of rent that returns are not constant, but diminishing. 3. The initial endowments in nonreproducible resources (such as lands) play a central role in the detennination of equilibrium prices and rents. 4. Prices and rents depend on quantities produced. The discussion of returns in the literature is often very confused, and it is useful to recall a few basic principles here. The notion of constant returns in the long term in each industry, does not contradict the existence of diminishing returns in the short term. Within a firm, productive capacities (the stocks of fixed capital) are given only in the short term, and diminished returns may be obtained if these capacities are over-utilized. The exemple of an assembly line is perfectly illustrative of this notion. It has been constructed to be used at some "normal" rate. Diminishing returns are met, if production reaches above-normal levels.3 With the exception oflabor, the rest of this book abstracts from the existence of nonreproducible resources. 3.3 Are profit rates equalized ? If one abstracts from nonreproducible resources, the classical theory of prices of production is what it ap-

40

Competition

pears, a straightforward characterization of a long-term equilibrium, with equalized profit rates among industries. It could be the case that this theory in its present crude form remains too abstract and simple to be used as a basis for empirical investigation, but there is no a priori methodological obstacle to the empirical test of the hypothesis that profit rates actually tend to gravitate around a common value.

In the following sections, we briefly introduce a few empirical results in this respect. Section 3.4 is devoted to Manufacturing and Trade, each of which are divided into two segments. Section 3.5 breaks down Manufacturing Durable into its components (nine industries) set forth in the NIPA data. The demonstration that profit rates tend to be equalized is typically hampered by a number of empirical difficulties and limitations: 1. The definition of the profit rate is crucial. We will show that by moving toward more and more relevant definitions, the equalization is constantly improved,4 but that empirical limitations are met because of data unavailability. In particular, it is impossible to consider the monetary and financial components of capital, which are not available by industries.5

2. The breakdown of enterprises among several industries is problematic. Petroleum provides a prominent illustration of this problem. One fraction (refining: etc.) is included within Manufacturing Nondurable, and another fraction (extraction) within Mining. The computation of the profit rates for the two activities clearly shows that the way the separation has been made is arbitrary. The profit rate for extraction is lower than the rate obtained for the average economy, whereas refining reveals a profit rate above the average.

Prices of Production

41

3.4 Manufacturing and Trade We consider four industries: Manufacturing Durable, Manufacturing Nondurable, Wholesale Trade, and Retail Trade. Three profit rates are determined: ( )

r 1 r

( 2)

r (3)

NNP - Labor income

= --------

Net stock of fixed capital NNP - Labor income

= ------------Net stock of fixed capital + Inventories = NNP -

Labor income - Indirect business taxes

Net stock of fixed capital+ Inventories

The results of the computation of the profit rates using these three definitions are presented in figures 3.1, 3.2, and 3.3, for r(l), r( 2 ), and r( 3) respectively. The series can be identified as follows:

l~x)

1:

Manufacturing Durable Manufacturing Nondurable Wholesale Trade Retail Trade

These results show very convincingly that the improvement in the definition of the profit rate progressively confine the profit rate dispersion to a narrower band. With r(l) the dispersion is very large, in particular in the early years for Wholesale Trade. In r( 2 ), the addition of inventories in the denominator eliminates a large proportion of the differential. The equalization is again improved when indirect business taxes are subtracted from profits, as in r( 3). In figure 3.3 it begins to be possible to contend that some form of gravitation around a common value is observed. However, it is also clear that this exercise should be extended to include other components of total capital. Unfortunately, data

Competition

42

Figure 3.1

Profit rates in four industries (1948-1985): - labor income)/ (net fixed capital)

r = ( NNP r(l)

2.25 2.00 1.75

·+., .•

1.50

. ·, .... · ·..... _.t., ....

1.25

·.........

1.00

"t.,_

.. * ·-· ·t

0.75 0.50

0.25 0.00-+-----r---..---..--...----....--T""-"-~---,

1945 1950 1955 1960 1965

Figure 3.2

1970 1975

t

1980

Profit rates in four industries (1948-1985): (NNP -labor income)/ (net fixed capital+ inventories)

r = r(2)

0.50

*

*

!·-. .... , ;. ··.,. .... · ·..................... ·. . .

"t·..

0.40

.

.

. .+.

.. .......

0.30

0.20 ~-·.

.

.•.·

.

0.10 0.00-+----..--...----....--T""-"--....--.----.----, 1945 1950 1955 1960 1965 1970 1975 1980 t

Prices of Production

Figure 3.3 r(3)

43

Profit rates in four industries (1948-1985): r = ( NNP - labor income - indirect business taxes)/ (net fixed capital+ inventories)

0.40

0.30

0.20

0.10

0.00-t---r--...-----.---..--""'T"--..----.----.. 1945 1950 1955 1960 1965 1970 1975 1980 t

on financial assets (and trade credits among industries) are not available by industry. 3.5 Manufacturing industries

It is possible to replicate the same computations as in the above section, for the "two-digit"6 industries of the manufacturing sector of the economy. For brevity, we present the results, for Manufacturing Durable alone. 7 The two definitions of the profit rate are r( 1 ) and r( 3 ): r( 1)

= __c_o_rp_o_r_a_te_p_ro_fi_t_ _

r(3)

= Corrected corporate profit -

Net stock of fixed capital Corporate profit taxes

Net stock of fixed capital

+ Inventories

The various aggregates used in the determination of the two profit rates are not fully consistent. This is

44

Competition

Figure 3.4

Profit rates in nine durable manufacturing industries (1959-1987): r =(profit)/ (net fixed capital)

.

r(l)

0.70]

:• •.•.

0.60 0.50 0.40 0.30 0.20 0.10

•·. . . -;.:-~·t;··...

.•

...:~·:\

0

;1:~:t·~~:~·f ;,D\.;;~i~. ...; •1.. ' •· ·. .a.-:•····i' •...

x·:. ..

·l··· .

"X.,x·

.__,

~····i-8-t.p.~ ~-o~ .. o·· "::".·_;a·_.~.··.~·~: ~:: ..... .,.-.~..... ~...o·· o

.J.1)(

.x· .x·

.

,'

>I"• :. ·,:f,·. ".+ ...•.a-~-'.·,g,:..:f. f" ·:a ~-·..- .,· ;e:,.,•

•.x:····).:.;'"····Jl.f.°.' ·" ·. ~· ·.·. ·............·"-~ ·:t•··.::.·. •

.

'X, ·X

.

..X

· 1'.,x,.X

-:"f. *· 1·

X· .X", "X. ? O, i.e., if too much capital has been invested in the first industry, then uh < u < u 2*, i.e., the capacity utilization rate in this industry is lower than the average. Note that this short-term equilibrium is an equilibrium by quantities alone, and not by prices. No prices are determined which allow for the clearing of markets. Instead capacity utilization rates are adjusted to levels which stabilize the level of inventories, i.e., equalize production and demand. As will be shown in the next section, the stability of short-term equilibrium can also be decomposed into two problems each with only two variables, bearing respectively on proportions and dimension in the short term.

Model

131

7. 7 The stability of short-term equilibrium The study of the local stability of short-term equilibrium concerns only the four short-term variables. The linear development of the model around short-term equilibrium is provided by the matrix M(10) in equation 7.7:

Ut+1 - U*) (Ut St -- U*) S* ( St+1 - S* _Ml V·t+l - U: St+l - S

-

(0)

u:

Ut St - S

An examination of matrix Mlo) reveals the existence of a 2 x 2 block of zeros in the upper right-hand side. This observation shows that the Jacobian can be written as the product of two polynomials of the second degree:

det (>.I -

M{o)) = ((>. - u)(>. -1) + e) ((>. - u)(>. -1)

+ eA)

The first polynomial corresponds to variables u and s (proportions), and the second to U and S (dimension). Consequently, the stability of short-term equilibrium can be decomposed into two distinct problems: 1. Stability in proportions. The first polynomial has two zeros which are either real and between u and 1, or complex conjugate. In this case, their moduli are smaller than 1 if: (7.9) 2. Stability in dimension. Since A is smaller than 1, the only problem concerning the second polynomial is the sign of this parameter (provided that condition 7.9 is satisfied). If 0 < A < 1, the moduli of the

132

General Disequilibrium

two eigenvalues are smaller than 1. If A < O, two eigenvalues exist, which are real, and one of them has a modulus larger than 1. A condition for the stabiliiy in dimension of short-term equilibrium is, thus, A > 0. This condition can be written: w < ( 1 - c1)

b-w) ( a-b1-

(7.10)

7 .8 Visible hands The problems raised by satisfying the two above conditions are quite different. Consider first condition 7.9 which governs stability in proportions. The polynomial (>.-u)(>.-l)+c- is, in fact, the Jacobian of a simple model of partial equilibrium in which a single enterprise, i, is considered and demand, di, is exogenous: i 1 Ut+

+ O' (Uti -

= -U

i+ Uti

i St+l =St

-

-) U - e ( Sti - -) S

di

This model corresponds to what might be called shortterm individual stability. We assume that this individual stability always exists. That one enterprise confronting a given demand is able to adjust its output to this level by the observation of the short-term movements of its inventories is, in fact, a very weak assumption about the rationality of behavior! Consequently, the stability of short-term proportions may be assumed. This finding is, in our opinion, very important. It provides an analytical basis for Smith's optimistic contention concerning the efficiency of decentralized economies. "Visible hands," though not necessarily very

Model

133

skillful, are sufficient to ensure the adjustment of proportions in the economy- at least in the short term. However, the above analysis also reveals the limits of this sanguine description of capitalism. The actual difficulties are met when the condition for stability in dimension expressed in equation 7.10 is considered. This condition has important implications from the point of view of the macroeconomy, which will be discussed in chapter 11. Note that, in the analysis of the stability of longterm equilibrium in the next section, we will assume that condition 7.10 is satisfied. For simplicity, we will 1- c1 I . f urt h er suppose t h at E > O, i.e., w < ci(l + y). n both cases, the point is to set a maximum bound to w.5

7.9 The stability of long-term equilibrium (as that of a sequence of temporary equilibria) The stability of long-term equilibrium can now be studied as a sequence of temporary equilibria. The shortterm equilibrium values of the variables as in equation 7.8 can be substituted in the linear equations of Xt+l and Yt+l (cf. equation 7.6). A recursion is obtained for the long-term variables: ( Xt+ 1 -

~) = N

Yt+l - Y

(

Xt -

~)

Yt - Y

The expression of N and its polynomial characteristic are presented in appendix 7.A3. The usual stability conditions are easily satisfied since f3 is small. An examination of the polynomial characteristic reveals a strong similarity with that obtained in section 6.3, in a far simpler model. This accounts, in retrospect, for the consideration of such simple models, and confirms the emphasis placed on the direct adjustment of quantities on quantities.

General Disequilibrium

134

7 .10 A summing up The results obtained in this chapter have far-reaching consequences which were difficult to anticipate, taking account of the still quite simple features of the model. They lie at the basis of the important typology of economic issues which will be introduced in chapter 9. The investigation of the existence and stability of the equilibrium of the general disequilibrium model considered in the present chapter shows that the conventional classical problem of the formation of prices of production, as analyzed in the previous part, actually refers to only one aspect-stability in proportions in the long term-of a more general problem. The overall analysis in this chapter led to the distinction of two additional issues concerning proportions and dimension, both in the short term, with quite distinct conclusions in each case. The stability in proportions of short-term equilibrium is subject to a weak condition. On the contrary, stability in dimension is subject to a condition which will be at the center of our investigation in the next part which is devoted to macroeconomics (and will be assumed to this point). In each case, the conditions for stability are defined for reaction coefficients. This means that, for any technology, demand function, or pace of accumulation (including a = p = O, or a = 1 and p = r ), a set of reaction coefficients exists for which stability is ensured. These conditions generally set minimum and maximum bounds to these coefficients. The issue of whether economic agents will actually choose the right reaction coefficients will also be reserved for a future section (20.1 ).

NOTES 1.

There is a Keynesian flavor in this mechanism because it is

Model

135

reminiscent of the accelerator. However, the two models are not identical. In our model, investment is a function of the level, Ut - u, of the capacity utilization rate, whereas the accelerator principle is based on the variation of output or of the capacity utilization rate Ut - Ut-l · Another approach, in which the expected growth rate of the capital stock is considered, is introduced in section 8.8. 2. If ( u! - u) is negative, the firm invests less than allowed by its financial resources and diminishes its borrowings or increases its financial investments. 3. The term -(1 - u) (u! - u) expresses three different types of phenomena: (1) The demand functions which enterprises confront are subject to random autoregressive shocks and only return slowly to normal levels (cf. Dumenil G., Levy D. 1990(a)), (2) In addition to traditional production costs, enterprises incur disequilibrium costs, such as the costs of stockpiling or the costs of changing production. The existence of these latter costs introduces some stickiness in the decision to produce (cf. Holt C.C., Modigliani F ., Muth J .F ., Simon H.A. 1960), (3) When u is large, enterprises accelerate their investment rate in order to ~ring their capacity utilization rate back to a normal level. 4. The assumption that /3 is not small would correspond to the model studied in the fourth section of appendix 6.A3. In this case the number of variables would be five for the short term, and one, y, for the long term. 5. One can notice that, in the absence of relationship between firms and banks, w = 0, and both conditions 7.10 and E > 0 are satisfied.

General Disequilibrium

136

APPENDICES 7.Al An analysis of stability based on the distinction between the short and long terms This appendix is devoted to the method of analysis of the stability of an equilibrium based on the distinction of two categories of variables: short-term variables, whose dynamics are fast, and longterm variables where the dynamics are slow. In order to compute the eigenvalues of the Jacobian matrix, it is possible to use a general metliod, known as the perturbation method (Wilkinson J.H. 1965). This method can be applied when the coefficients of the Jacobian matrix are functions of a parameter assumed to be small. The computation is based on a development in this small parameter. If one is content with the first-order terms, it is possible to show that the perturbation method is equivalent to the method of temporary equilibrium, which lends itself to economic interpretation. With this latter method, the overall dynamics are decomposed into short-term dynamics and long-term dynamics, and the stability problem can be decomposed into two components: 1. The stability of the short-term equilibrium (temporary equilibrium). 2. The stability of the long-term equilibrium (as a succession of temporary equilibria). The rest of this appendix is devoted to a brief presentation of the method of temporary equilibrium. Consider X E R" which follows a linear relation of recursion:

We decompose X into two vectors, Y and Z, corresponding to two groups of variables, short-term and long-term variables respectively:

X =

(~)

with

YE Rm

and

Z E R"-m

A decomposition of matrix M into four matrices corresponds to

137

Model this division: M1 M= ( Ms

M2) M4

Thus, the recursion can be written:

Yt+1 = M 1 Yt

+ M 2 Zt

Zt+1 = M 3 Yi

+ M 4 Zt

(7.11}

We assume that the elements of M are functions of a parameter, = 0:

T/, and can be developed in the vicinity of TJ

M

= M(o) + TJM(1) + TJ2M(2) + · · · = (

M~)

M(o)

M(o)) M(o)

+ T/ ( M~)

.M(l)

M(1)) M(l)

+ ...

By definition, the long-term variables, Z, are constant in the short term. Thus, M(3o) = 0 and M~) = I, with I denoting the identity matrix. The temporary equilibrium corresponds to the computation to the order 0 in TJ of system 7.11: Yt+i = Mlo)Yt

+

M(2o)Zt

Zt+ 1 = Zt

The short-term equilibrium of Y is Y* = (I - Mlo))- 1Mf0 )Z, with Z denoting the constant value of Zt, and the short-term dynamics can be written:

The stability of this recursion depends on the eigenvalues of Mlo)· This problem is now more easily tractable than in its original formulation, on two counts: 1. The dimension is now m, instead ofn. 2. In the general case, Mlo) is much simpler than M 1 . Consider now the long-term dynamic-s (the succession of temporary equilibria). The dynamics of Z to the order 1 in TJ can be written:

General Disequilibrium

138

Since the short-term dynamics are fast, we can assume in the analysis of long-term dynamics that l't has converged toward l'*. Importing Y* in the above equation, we obtain: Zt+i = NZt with N =I+ T/ ( M(1 ) + M(1 )(J - Mto))- 1 Mc2o)) The stability of long-term equilibrium depends on the eigenvalues of matrix N, whose dimension is n - m.

7.A2 Short-term dynamics The first purpose of this appendix is to make explicit the notation used in equation 7. 7:

(1'

i

(

A

o

2

c0

00 )

Meo)= ( 0 0 -B D u/fj Since the calculations are made to the order 0, the expressions of the equilibrium values of the variables can be simplified: _ cS+F ;; = u(b - u) - c5 y = b- 6 _ u- -p Meo)=

Equations 7.8 are derived from the following equation which expresses the equilibrium of recursion 7. 7:

139

Model The auxiliary notation E in equations 7.8 is:

-1+-

E = (1- a)~

y

y

(1 - c1

c1 (1

-

+ y)w)

7.A3 Long-term dynamics This appendix presents the expression of N and of its polynomial characteristic: N- ( -

with

-/31 - o- i

1 - /3 l - o- E

e A bEF -yy--y

e y 1 - pii y

)

F = (-y(b - w) + wb)y

>. -

1 - O'/3 -e-u

1

det(>.I - N) =

--rbu

>. -

1+

p!y + E13l - oA e

Developing the two eigenvalues as functions of f3, one obtains:

>.1 =

u

1 - F= y

+ (· · ·)/3 + · · ·

>.2 = 1 - -r 1 - o- buy /3 + (... )/32 e

F

+ ...

The moduli of these eigenvalues are smaller than 1, since /3 is small.

8. Development of the Basic Model The construction of a model such as that presented in the previous chapter requires a strict discipline, and there is an obvious trade-off between complexity and manageability. In spite of the progress made in chapters 6 and 7, the framework remains simple in many respects, and some of the assumptions severe. Our experience in publically presenting such models reveals that most people have a sense of what is missing -and is essential-in these frameworks. The tantalizing promise of the modeling of the classical analysis of competition is marred by the still rudimentary character of the models; the economy is centralized, since only one capitalist exists; only one firm is considered in each industry and, therefore, there is no real competition on the market; convergence is possible, only because technology is identical in the various industries; real problems occur as soon as more than two industries are considered. How can one abstract from rationing ? What about technological change, the variation in tastes, and nonhomothetical growth? What about money and credit? etc. The work of classical economists is a bright demonstration of the power of abstraction. '\iVhen they described the working of competition, they ignored a very large set of difficulties, in particular, many of those listed above - and this is what renders their analysis understandable to the reader. It is true, however, that all of these points are relevant 140

Development of the Basic Model

141

in some respects, and cannot be dismissed with a hand wave. The purpose of tlris chapter is to address some of these issues. Many of these developments of the basic model would be difficult to handle analytically. For this reason, the investigation relies on computer simulation. With this method, it is possible to be less restrictive, and to rapidly survey a broad variety of issues. In this investigation we will ignore all considerations related to stability in dimension and focus on proportions in tl1e long term, i.e., the original classical investigation, and only briefly illustrate the notion of short-term equilibrium. This chapter demonstrates the robustness of the classical analysis of competition. This analysis of long-term equilibrium and its stability provides a very promising framework on which to build sophisticated analyses. Stability can always be obtained, under specific conditions on reaction coefficients. 8.1 Relaxing assumptions

The first simulation uses a model very close to that in chapter 7, but in which a number of simplifying assumptions have been relaxed: 1. Three goods and three capitalists exist. 2. Technology is different in the production of each good. 3. The reaction parameters and target values of every agent (the three capitalists and three firms) are different. The two first issues have been previously discussed in the literature. It has been cont~nded, for example, that the tendency to equalize profit rates may be frustrated, if more than two goods exist, because of the paradoxical effects of prices on profitability (Steedman I. 1984). If the price of a commodity is relatively high, this does not ensure that the profit rate is also relatively high, because

142

General Disequilibrium

of the price of inputs. In connection with point 2, in Nikaido's papers (1977 and 1983) stability is subject to a condition on technology. In the model studied here, the three commodities correspond to fixed capital, a circulating input (or raw material), and a consumption good. The three capitalists can invest in the three firms, that they jointly own, as suggested by the diagram below. The capitalists allocate their funds in these firms according to the respective profit rates which each capitalist compares with his own average profit rate for all of his investments. A new variable 11:,j denotes the share of each firm i owned by capitalist j, with L:j 11:,j = 1. These shares of ownership are progressively modified, as a result of capital mobility. The profit of the enterprises is then divided among the capitalists in proportion to their share of ownership. Capitalists:

•

•

•

Industries:

•

•

•

We abstract from the direct relationship between firms and the banks (section 7.1.8). The rest of the model is similar to that in chapter 7 (except that technologies, reaction coefficients, and the target values of the variables are different for each agent). Only the a:j s, the shares of profit accumulated by each capitalist, are supposed to be identical. If this assumption is not made, the capitalist with the larger a: will progressively dominate the entire economy (since each capitalist has his own relation pi = air). A continuum of equilibria exists in this model, since the shares of ownership can take any value when equi-

Development of tbe Basic Model

143

librium is reached, depending on their initial values and of the exact trajectory which preceded the equilibrium. For the other variables, a classical equilibrium is attained with prices of production and given proportions of capital among firms. The target values of the capacity utilization rates and rates of inventories are reached. Figures 8.1and8.2 present the results of a convergence obtained with this model for the profit rates of the three firms, and for the shares of ownership of firm 1: 77 1 •1 , 771,2' and 771,3. The stability property of this model is robust. Stability can be obtained for a= 0 (simple reproduction) and a = 1 (maximum growth rate), as well as for any intermediary value. It is also possible to check the effects of different capital/ labor ratios T. Seven cases have been successfully investigated: Tl < T2 < T 3 , Tl < T 3 < T 2 , T 2 < T 1 < T 3 ' .. ·, and T 1 = T 2 = T 3 . One also can verify that. a number of technicalities can be changed with no significant impact on the stability condition: (1) Wages can be paid ex ante or ex post, (2) In the computation of the profit rates, circulating inputs and inventories may be included, or not included, in total capital, (3) Reaction functions can be nonlinear, ( 4) The price equation can also include a term in u~ - ui, (5) Prices can be determined by a markup above cost, with a mark-up rate modified in response to the disequilibrium between supply and demand (see appendix 8.Al), and (6) Capitalists can utilize past or expected profit rates (with extrapolative or adaptive expectations) in their evaluation of profitability differentials. 8.2 Stability conditions

It is important to distinguish between the two notions of stability of an equilibrium and stability of a model. We use the first expression, stability of an equilibrium, in the conventional sense, as recalled in section 6.2, of

General Disequilibrium

144

Figure 8.1

Three capitalists and three firms: profit rates of the three firms

.,. 0.80

..

0.70

..

'•

0.20

..

0.10

..

o.00----.-----.--..---"'T'"'"---T"----..---....----. 20 40 60 80 100 120 140 t 0

Figure 8.2

Three capitalists and three firms: shares of ownership of firm 1

.,, 0.55 0.50 -.... ..·-···-.......... / ·....·· ···..........·' 0.45

,......·..

······............

.....······-...........

......-.....

·····-········

.,,1,2

··................

0.40 0.35 0.30 _.............._.....-..........- .................................................................................................!1~~.~..

0.15-+----.-----.--..--"'T'"'"---T"----,r---....----. 60 80 100 120 140 t 0 20 40

Development of the Basic 1'.fodel Figure 8.3

145

Stability conditions: r 1 for three values of coefficient c

1.40 1.20 1.00

:, .... : :. .·:(3) ....

, "

0.80

...

~:

0.60 0.40 0.20 0.00

. '. ...

' -0.20-+----.---..----.----.--....---.----.r---. t 0 40 80 120 160 200 240 280

local stability. Beginning with initial values of the variables different from equilibrium, will these variables evolve toward their equilibrium values? "Local" refers to the fact that the initial values of the variables must not deviate too strongly from their equilibrium values. In other words,. convergence is limited to a particular convergence region. The problem is different when we discuss the stability of a model. We provide this notion with a quite specific meaning, which echoes our analysis of behaviors in terms of disequilibrium microeconomics. The "core" dynamics of our models are the description of the agents' behavior in reaction to disequilibrium, in which the degree of the response is measured by reaction coefficients (such as u, c, {3, {, ... ). All other parameters, for example, describing technology, should be denoted as structural. A model is stable if, for any values of structural parameters, one can locate sets of values of the reactions coefficients which ensure the (local) stability of equilib-

146

Ge11eral Disequilibrium

rium. In the general case, these values are moderate, neither too weak, nor too strong. Thus, st.ability is always conditional in two respects corresponding to these two notions, stability of an equilibrium and stability of a model. Limitations are set for both the initial values of the variables, and the reactions of economic agents. These limitations are relevant in the real world: 1. Capitalist competition has an ability to control the

proportions of prices and outputs, but this ability is not absolute. Beyond a certain point, disequilibrium can result in more severe perturbations. The contention that convergence must be ensured under any initial conditions would be a caricature of the functioning of capitalism. It is easy to find examples of violent perturbations, such as real or commercial wars, which can only be overcome following lengthy and painful periods of adjustment, which often require a degree of state intervention. 2. As already mentioned in chapter 6, the idea that there exist upper and lower bounds to reaction coefficients which maintain convergence is quite intuitive. A weak reaction may be insufficient to counter the increase in disequilibrium. Too strong a reaction can create a new disequilibrium of opposite sign and possibly broader than the original. Recall the driver metaphor evoked in section 6.2. If the car moves to the right, the driver must turn the wheel to the left, and vice versa. Deficient as well as excessive reactions could be fatal. The size of the interval must be discovered from learning and experience. The same is true concerning the management of capital or firms. Figure 8.3 illustrates the effect of different values of coefficient e (which measures ihe sensitivity of output to inventories) on stability. The movement of the profit rate in the first industry has been plotted for three different values of e. In the first case (1), convergence is obtained with an appropriate value of e. In the second

Development of the Basic Model

147

case (2), e is too low and a limit cycle is observed. Note that this is not a representation of the business cycle, but a "gravitational cycle" in proportions. In our opinion such movements have little factual relevance. In the third case (3), e is too large and an exploding trajectory is observed.

8.3 Gravitation and rationing The basic model of chapter 7 is a model of convergence. In such a model, the economy begins out of equilibrium, and the study demonstrates the ability to move to the equilibrium position, in the absence of further perturbation. This model studies the centripetal forces which pull the economy back to equilibrium, the central aspect of the classical paradigm of competition. However, recurrent perturbations (centrifugal forces) force the economy into a constant gravitation around the equilibrium position. A state of gravitation is a "stationary" (but agitated) regime in which centrifugal forces are matched by centripetal convergence forces. A model of convergence can be easily transformed into a model of gravitation with the introduction of shocks. In the simulation described in figure 8.4, demand is randomly shocked in the three industries. The expected result is obtained, and one can observe a gravitation of the three profit rates around their common equilibrium value. There is a direct relationship between the speed of convergence toward equilibrium in the absence of shocks, and the amplitude of the gravitation of the variable around its equilibrium value, when exogenous stationary shocks are added. For the same shock amplitude, a faster convergence would lead to a gravitation of lesser variance, and conversely for a slower convergence. This result is quite general and would be observed in other models when random shocks are added. All of the simulations in this chapter that distinguish between

General Disequilibrium

148 Figure 8.4

Gravitation: profit rates

r

..

: ":

0.60

. . ..f\

::

:

:

:

~

....

0.50

.:·.

.·

...

0.40 0.30

·.·

·.:

·....

0.20 0.10 0.00-+----.---.----.----.---..----.-------. 40 80 120 160 200 240 280 t 0

Figure 8.5

Rationing (under gravitation): the ratios of inventories

8

0.45

...

0.40

.. .. f ~ . .

0.35 0.30

...

I\

:·=

0.20

.....

::

:~ I ~ 1:

0.15 0.10

..

=~

~

:

: :.

:. : .:. : i

:

:

: : : :'

f\}

:.: n

0.25

. . ::

..

.. . : ·.. ·......

\/\

\;"

\/

::':

: . ·':

...

·.:

·. . . / .!\.\_._! ::

••

:":

: . .J: :. .

I:

. .A..ft\.·.·_::_:i :=-"\:\:f·.?\i :/~:\

~-: . .r.A_.,:F \ . . . ..

r\ f \

:-:.:-·. : : : :

..' ::

2

t\

\f \.! :~·

\ . .../ \)!:..!"~~. .: ; .. .f.1 .J\.J -.-----.---.-------------. 0 .00-+----P~.....:'--"":...... : ·,. . ;·.·_.'_·.....-...=.................

0.05

0

40

80

120

160

200

240

280

t

Development of the Basic Model

149

fast and slow convergence processes can be interpreted in terms of gravitation of various amplitudes. For example, if two profit rates converge rapidly toward equality, whereas the third rate is only slowly equalized, this means, in fact, that the two first rates will gravitate at a small distance from one another, whereas the third one will gravitate with larger deviations. If the economy is dramatically shocked, inventories may be driven to zero (in spite of the buffer of inventories that firms attempt to maintain). If inventories are allowed to become negative in the model, convergence is not hampered. But the existence of negative inventories lacks realism. From the point of view of the seller, negative inventories can be interpreted as unfilled orders, but the activity of the buyer would be limited, in any case, by the unavailability of an input. In the simulation described in figure 8.5, the consequences of rationing are treated in the following manner. If the stocks of inventories of capital goods or raw materials are exhausted, the purchases by the three firms are diminished in proportion to their demands. The rationing of raw materials sets a limit to production. Conversely, the lack of availability of fixed capital is corrected by an increased utilization rate of existing capacities. If rationing affects the consumption goods, the unused purchasing power is transmitted into the next period. (This requires the introduction of a new variable which differs from zero when rationing occurs for the consumption good.) Figure 8.5 presents the results of a model with gravitation such as that used in figure 8.4, but the size of the shocks is larger, and rationing may occur. The target ratio of inventories in the firm producing consumption goods is larger than those in the two other industries, and no rationing is observed for this commodity. Conversely, inventories sometimes shrink to zero in the two other firms. Rationings of raw materials delay production, but one can observe in the figure that they are corrected after some time. Globally, a gravitation with

150

General Disequilibrium

recurrent rationing is observed.

8.4 Intraindustry competition The aspects of the competitive process which are studied below can be organized around the distinction between the effects of competition within a particular industry (intraindustry competition) and these effects among industries (interindustry competition): 1. In the former case, the issue is that of the interaction of different producers within a single market. Intraindustry competition explains how a common price for homogeneous commodities finally prevails on the market, on the basis of decentralized price setting. 2. Interindustry competition leads to the formation of an equalized profit rate between industries. An important aspect of these mechanisms is that they unfold at different rates. Consequently, the various outcomes are obtained successively at different stages in an overall process. Marx had a remarkable insight into these properties: What competition brings about, first of all in one sphere, is the establishment of a uniform market value and market price out of the various individual values of commodities. But it is only the competition of capitals in different spheres that brings forth the production price that equalizes the rates of profit between those spheres. (Marx K. 1894, Ch.10, p. 281)

In this passage, Marx identifies the two separate processes at work: the formation of a unique price for each commodity and the establishment of a uniform rate of profit among industries. In the model used to investigate these two aspects of competition, only one capitalist and two commodities exist, but three distinct enterprises produce each commodity within each industry, as shown in the diagram below. In this section, we assume that the three

Development of the Basic Model Figure 8.6

151

Intraindustry competition: prices

1.30 1.20 1.10 1.00 0.90

{\: ::! . •.

·.

.·. .w·:·::··.

·V\~-.:_:i.:-;:::~.:::.::::·7:-r · · ··= ·;~·-............................ · ····•·•·····• ··•······•· ····· ·

"\l../\ .. \.. ~, ..r..l(;~, . ,... :~·.

/:~

t~/

0.80

., ,

J

.....t . 11....

..... ..

••••

........

.. ....................................

•

0.70-+-~"T""""~"T"'""~-r-~-.-~..--~..-~..-~....-~....----.

0

50

100 150 200 250 300 350 400

450

t

Figure 8. 7 Intraindustry competition: profit rates r 0.014

.· ...

0.012 0.010 0.008 0.006 0.004 0.002 O.OOO-t-~"T"'""~"T"'""~-.-~-.-~-.-~..--~..-~..--~....----.

0

50

100 150 200 250 300 350 400 450

t

General Disequilibrium

152

producers, acting within the same industry, use an identical technology.

•

Capitalists:

Firms:

•

4~ •

•

•

•

•

In spite of the small number of capitalists and goods, this model is already rather complicated since it consists of a total of 22 variables. In this framework, it is necessary to model intraindustry competition among the sellers of the same good. To do so, we adopt the point of view of monopolistic competition ( c£ section 5.5), in which buyers differentiate among the various sellers within the same industry, yet are sensitive to price differentials. In this model, the demand facing a particular firm is influenced by the behavior of all other firms within the same industry, but in a simple manner, only via the average price in the industry: the demand faced by each firm depends linearly on its relative price within the industry. The demand to firm l ( l = 1, 2, 3) in industry i (i = 1, 2) is denoted Di,l. This firm sells its product at a price pi,l. Di denotes the total demand to industry i, where the average price is pi- = :L:f=l pi,l. With this notation the demand function to firm (i, l) can be written:

l

(8.1) In this equation, cp denotes the slope of the demand function, and measures the intensity of competition. A large

.1 > ll>-2,311) and close to 1.

Macro (In)stability

211

11.7 Business fluctuations

The instability of the general level of activity is a striking feature of capitalist economies, and in sharp opposition to its stability in proportions. It is manifested in the variations of the general level of activity, which is alternatively smooth and then subject to swift variations (in particular, downward). For all its crudeness, the model presented in this chapter reproduces a number of interesting features of business fluctuations. Mathematically speaking, instability in dimension corresponds to the fact that the dominant eigenvalue is close to 1, and can easily become larger than 1. This eigenvalue depends on all the parameters in the model (reaction coefficients of firms and of banks, in particular), so there is no single cause to overheatings and recessions, but rather a broad variety of triggers. The economy remains constantly close to the stability limit, like an object on the edge of a table waiting to fall at any instant. Thus, the destabilization of the general level of activity is recurrent, but not cyclical in the strict sense of the term (i.e., repeated with a given periodicity). An important prediction of our model is that there is a covariation between the fluctuations of output and inventories (equation 11.8). Since A = 1.021 and u = 0.913, A- u is positive and t.his covariation appears as a trade-off. This trade-off is related to the eigenvector associated with the dominant eigenvalue and describes the "dominant" behavior (i.e., the main features) of the two variables u and s out of equilibrium. Along this trade-off are manifested simultaneously: the usual gravitation of the variables, business fluctuations (overheatings and recessions), and the shifts of equilibrium (due to policies in particular). It was already clear from figures 11.1 and 11.2 that the directions in the fluctuations of u and s around their trends are opposed. The scatter diagram for the

Business Fluctuations

212

Figure 11.3

The trade-off between the Buctuations of output and inventories, the example of the 1970s

ut 0.075 0.050 0.025 0.000 -0.025

··. ~....

:

..··.. . .. ·. . .-.··..... . . . . . . . i·" ,._ .

...........

..............~

.......... .............

.............

•

-0.050

.. : . . ..

.- ~ ~-···~.................... : ··.· . ....... •

•

•

... ;··....

..~··!

•

·~· ...............

...............

-0.075 -0.100 -0.125-i---~------~----~---~ -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 Bt-1

Inventories are leading by one month. The variables used in the scatter are 11.t and Bt-l·

same period is presented in fi~ure 11.3. The correlation coefficient is equal to -0.74 {with a lag of 1 month on s ). One should notice that the reference to a negative correlation between output and inventories of finished goods in the modern literature is rare. It is not mentioned, for example, in Victor Zarnowitz's authoritative study of the business cycle (1985). The work of Moses Abramovitz (1948 and 1950), however, is an exception. More attention has been devoted to total inventories, which move procyclically, than to the inventories of finished goods considered here, which move countercyclically. Conversely, economists in the 19th century had already identified this trade-off. They had observed that inventories of unsold commodities increase when output begins to decline in a recession. Crises used

Macro (In)stability

The :fluctuations of output (• j and employment (o) in manufacturing industries (1953-1989)

Figure 11.4 u,h 0.100

213

.. 0

0.075 0.050 0.025 0.000 -0.025 -0.050 -0.075 -0.100

t The fiuctuations of employment have been divided by 0. 794.

to be designated as crises of "overproduction," for this reason.

11.8 Fluctuations in employment In the model presented in this chapter no variable has been introduced to account for employment, since employment is assumed to be strictly proportional to output. (Note that it would have been formally equivalent to conserve employment and eliminate output.) This choice follows from the observation that, in the short term, the fluctuations in employment reflect the general level of activity. Obviously, this view cannot be extended to the trends of the variables over longer terms, which are functions of the transformation of technology (in particular, the rise of labor productivity). It is well known that the fluctuations of employment

214

Business Fluctuations

do not respond immediately and fully to those of output, and this is manifested in what is called the productivity cycle. When output diminishes in a recession, for example, the number of hours worked is also reduced, but to a lesser extent and with a lag. This does not alter the very strong correlation between the two variables. The correlation coefficient still equals 0.96 ! This is illustrated in figure 11.4, where the two fluctuations, Ut for output and ht for employment, in manufacturing industries, have been ploted.9 Of course, a strong negative correlation exists between the fluctuations of employment and unemployment. The fluctuations of unemployment are the inverted image of those of employment, and consequently those of output. (This latter relationship is known as Okun Law, cf. Okun A. 1962.) This correlation takes on special significance, since it means that the explanatory power of the model can be extended to unemployment. It is not possible, however, to document this relationship within Manufacturing, but the same methodology as above can be applied to the total economy. The correlation coefficient for the fluctuations of output and unemployment is -87 percent. The observation that this correlation coefficient is less strong shows that the variations of the labor force ("labor supply") has an influence in the short term.

11.9 The role of money (and credit) In our analysis of business fluctuations, the overall stability of the economy is the outcome of individual and macroeconomic mechanisms, both real and monetary. Money plays a central role. Firms can create or destroy purchasing power, resorting more or less extensively to trade credits, and banks can issue money, but there is also an important macroeconomic component corresponding to the control of money and credit. In the early stages of capitalism, this control was en-

Macro (In)stability

215

sured t.o a certain extent by "market" procedures,10 through gold during the Gold Standard and, to some degree, as a result of the early forms of organization and self-discipline of monetary institutions. In modern capitalism, this control is imposed within a complex institutional framework, at the center of which stands the central bank, i.e., in the US, the Federal Reserve. There is no simple rule concerning the effects of real or monetary mechanisms. Some are stabilizing, and others destabilizing. There are four distinct yet interdependent aspects of this question: 1. Firms' reaction to the disequilibrium between supply and demand, as in equation 11.1, is a real determinant of stability. It is destabilizing, as expressed by the chain, low output -t low demand-t lower output, when demand falls short of supply. 2. The autonomous return to "normal" of the capacity utilization rate as measured by u is a real stabilizing determinant of stability (stronger when u is smaller). 3. The first term in equation 11.4, which accounts for the propensity and ability of firms to borrow (or resort to trade credits) is a monetary determinant of stability. It is destabilizing: large output -t stimulation of the issuance of money-t stimulation of demand-t larger output. 4. The reaction of monetary authorities to inflation is stabilizing: in:Bation -t reduction of the issuance of money-t reduction of output -t diminished in:Hation. Money is not neutral, but it is not the villain that it is often portrayed as either. Money also impacts on the determination of equilibrium.11 The supply behavior of firms that attempt to reach the target values of their variables (capacity utilization rates and ratios of inventories) is not sufficient to guarantee that these targets are actually attained. Demand also plays a role in this respect. Money and credit allow for the equality between the equilibrium

216

Business Fluctuations

values and these individual target values. If the mechanisms through which the issuance of money is ensured are disconnected (i.e., assuming that Mis constant, with d = e = 0), and if prices are constant (i.e., a= {3 = 0), then the above equality is not. obtained, and the equilibrium values are: M

Y*

=

a+cP

1-b

and

S* = S - 1 - u (Y* - Y) e

We say that equilibrium is not "normal," but shifted (or "Keynesian").

11.10 The role of institutions The use of the term "behavior" to account for the reaction of firms or banks is, to a large extent, misleading. It overlooks the fact that these agents are actually complex institutions. The notion of optimal behavior must be considerably qualified in this respect )2 In the analysis of the stability of the overall level of activity, the point at issue is not the optimal character of firm behaviors, but that of monetary institutions. Taking the behavior of firms as given in condition 11.7, it appears easy to determine an appropriate degree of reaction on the part of monetary institutions (i.e., an appropriate value of its reaction coefficients). If the destabilizing charact.er of the reaction of firms is increased, one must modify the functioning of monetary institutions! Considering the entire dynamic system (not only equation 11.7), it is even possible to define optimal reaction coefficients, i.e., those which ensure the fastest convergence. This point of view is based on a fundamental misinterpretation of the nature of the mechanisms represented in the model by equation 11.4. The control of the Federal Reserve over the macroeconomy operates through a

Macro (In)stability

217

broad and complex framework of laws, regulations, and policies. Information must be collected efficiently, and the decisions must be followed up by the actual modification of the behavior of numerous individual financial agents. This means that considerable institutional reformation is implied in the modification of coefficients d and e. Inertia is a well-known characteristic of institutions, and many diverging interests are involved. Laws, regulations, and policies are usually transformed as a response to the manifestations of actual maladjustments, and repeated attempts and rectifications are always required. The issue is not that of the choice of an optimal procedure, but the historical progress of the social control of stability, an always difficult process. As is well known, the debate surrounding these transformations is highly imbued with politics.

NOTES 1. 2. 3.

4.

5.

The analysis in this part borrows from Dumenil G., Levy D. (1991(c)). Production is not equal to the demand expressed during the period, as in a Keynesian model. The effects of the movements of prices on monetary policy are well established for contemporary capitalism. The Federal Funds rate is modified in response to the variations of prices, and impacts on the general level of activity (see Bernanke B., Blinder A. 1990). For simplicity, our model directly considers the stock of money, and abstracts from interest rates. A more sophisticated modeling of money and credit or the representation of earlier procedures clearly oversteps the limits of the simple model used here. The nondiagonal terms in A in the determinant are related to the existence of variables indexed in t, instead oft - 1, in the right-hand side of the recursion 11.6. One has: P(l) = c((l - u)C - eB). Since the coefficient of the term of larger degree of polynomial P(A) is positive,

218

Business Fluctuations

A< 1 requires P(l) > 0, i.e., 8 < 1. We begin the series in 1953, after the Korean War, because of the abnormal fluctuations of inventories in the aftermath of World War II. 7. Using quarterly data, the correlation coefficient between the fluctuations of the two gross products is 0.96. 8. We use the method SUR (Seemingly Unrelated Regressions or Generalized Least Square) of the SYSLIN procedure in SAS. The figure within parenthesis is the Student's t. 9. With Ht denoting the number oihours worked by all persons engaged in Manufacturing, ht is defined as ln Ht - ln Ht· 10. We refer here to the withdrawal of gold from the banking system during periods of inflation, and to the stabilizing effect of imports and exports of gold in relation to the disequilibria in international trade. 11. Cf. section 3 of appendix 11.Al, which also discusses this issue. 12. This was already briefly discussed in section 10.5.

6.

Macro (In)stability

2:!.9

APPENDICES 11.Al Reconciliation of the models as in parts III and IV The purpose of this appendix is to compare the model witl1 one good used in this chapter, with the models with several goods used in the previous part. 1. Assumptions and equations

Equation 11.2 is more general than equation 7.4, since prices are also modified on the basis of disequilibria in capacity utilization rates. In the model with two goods of chapter 7, we assume that prices are sticky (/3 small), and may be assumed constant vis-a-vis shortterm dynamics. In the present chapter, the time frame is also short term, and a and /3 are supposed to be small. This does not mean that the reaction of monetary authorities to the variation of prices is inefficient. Consider the expression for (} in the stability condition 11. 7. We assume that a and /3 are small, but not the two products ae and {3e. This means that the impact of the real balance effect, corresponding to a and /3, is small, whereas that of the issuance (and destruction) of money is not. In both models, in chapter 7 and in the present chapter, there is an element of stickiness in demand. In equations 7.2 and 11.3 this stickiness is represented by the two terms coYt and a+ c*, which are stocks, whereas the two other terms are flows and move procyclically. The time indexes are not exactly identical (as in equations 7.3 and 11.1). In the present chapter the Jags have been determined on the basis of the estimate of the model. (St instead of St-l in equation 11.1 probably indicates that one month is still a long period.) 2. The stability condition (dimension in the short term) In chapter 7, the stability condition is expressed in equation 7.10. Using equation 7.5, and with the short-term approximation, this condition can be written: w

< co(l +ii)

220

Business Fluctuations

With a = 0 and f3 . ~

t=l869

((zt - "Zt-d - (zt-1 - "Zt-2)) 2)

t=l871

s.t. a:t = 'Zt + Zt This allows for the construction of a more or less rigid trend, depending on the value of parameter .>.. This means that a compromise, depending on .>., is made between the distance of the variable to its trend (the fi.rst term) and the curvature of the trend (the second term). In the investigation of the short-term fluctuations of the variables, we use .>. = 15000 for monthly series and 1600 for quarterly series as is conventional. In the investigation of historical tendencies, a larger value of.>. is required to obtain a more rigid trend. We choose .>. = 5000 for annual series.

12. The Impact of the Profit Rate on the Macroeconomy In the previous parts of this book, the emphasis has been placed on the importance of profitability for proportions in the long term. Profit rate differentials direct the allocation of capital among industries (whereas disequilibria are corrected in the short term, by the adjustment of capacity utilization rates). In the present chapter, we contend that the impact of the profit rate is also felt with respect to dimension in the sl10rt term. The profit rate affects the stability of the macroeconomy, and low profitability levels are reflected in the larger amplitude of business fluctuations.I The investigation in this chapter is primarily empirical. The ma.in question to which this chapter aspires to make a contribution is the effect of the profit rate on business fluctuations in general, but we will also attempt to identify more precisely the channels through which this influence is transmitted. Stability in dimension is the outcome of the reciprocal relationship between supply and demand-from supply to the formation of demand, and from demand to the decision to produce, including the impact of money and credit in the formation of demand (for consumption or investment). The question is whether the influence of the profit rate is felt through supply or demand mechanisms. As we will show, profitability affects mostly the supply behavior of firms, specifically the response to disequilibria between supply and demand. This finding can be interpreted in relation to the effect of profitability on firm liquidity (and not indebtness as might be ex224

The Impact of the Profit Rate

225

pected), and points to a further impact of money. A last section will also discuss the notion of a minimum profit rate, which follows from this analysis. The choice of a. specific measure of the profit rate is an obvious preliminary to this investigation. A definition of the profit rate rather "close" to the firms' bot.ton1 line is required. Therefore included in the capital stock are fixed capital and inventories, and profit is measured net of interests and t.a.xes. The unit of analysis is the corporate manufacturing sector. A more precise definition and the plot of this profit rate are provided in section 1 7.4.

12.1 Does profitability impact on stability? In order to test for the influence of the profit rate on stability in dimension, we will use the macroeconomic model introduced in the previous chapter. The problem is to determine whether the profit rate affects the value of the parameters in this model and, consequently, the dominant eigenvalue. In chapter 11, the number of equations had been reduced from three to two, by eliminating the monetary variable (cf. section 11.5). It is possible to set aside a second variable and work with only a single equation. To this end, we e~iminate s from equations 11.9 and 11.10, and express u as a function of its own lagged values: (12.1)

In this equation D, E, and F are functions of the reaction coefficients, u, e:, a, (3, d, and e, and of the parameters in the demand function, b and c. If any of these parameters is a function of r, the same is also true of D, E, or F, and of the dominant eigenvalue. We will estimate the above equation with a dependence on r for parameters D, E, and F: D = Do+ D1 rt,

Business Fluctuations

226

and the like for E and F. 2 From the point of view of econometrics, this is equivalent to the introduction of interaction terms such as rtUt-1' rtUt-2, etc., in addition to the original variables Ut-1' u1-2, etc. The most significant combination (i.e., that which yields the most significant Student's t on the interaction terms) is the following (R 2 = 0.91): Ut

= ( 1.21 Ut-1 - 5.35 TtUt-1) (t=25.5} (t=2.6}

+

4.24

(t=2.0}

TtUt-2) -

0.154

(t=3.3}

Ut-3

+ (-

0.154

(t=2.1}

Ut-2

(12.2)

With this estimation, one obtains D = 1.21 - 5.35rt, E = -0.154 + 4.24rt, and Fis a constant. Stability is obtained when the three roots of polynomial >. 3 - D>. 2 - E>. - F have a modulus smaller than 1. (This condition is identical to that concerning the roots of the polynomial characteristic in section 11.4.) Since the dominant eigenvalue, A, is real and close to 1 (i.e., 1-D - E-F is close to zero), it is possible to provide an approximation of this root:

1-D-E-F

A=l------3-2D-E

(12.3)

Stability is basically determined in this equation by the value (and sign) of 1-D-E- F (since the denominator is positive). The dominant eigenvalue diminishes when this expression increases. Parameters D and E are functions of r, and the same is true for 1- D - E - F. In this expression, utilizing equation 12.2, the coefficient of r is 5.35 -4.24 = 1.11, i.e., is positive. Consequently,

a larger r diminishes A and, thus, improves stability. This result fully confirms our basic hypothesis that profitability impacts on stability, larger profit rates being associated with an improved stability.

Tl1e Impact of the Profit Rate

227

It is possible to test for the robustness of this result by comparing the profit rate with other variables. The same procedure as above has been repeated for various measures of the rate of interest,3 in isolation or in combination with the profit rate. The rate of interest is never significant.

12.2 How does profitability impact on stability? In the present section, we discuss the mechanisms whereby this impact of the profit rate is transmitted: supply or demand sides? Who are the agent.s whose behavior is affected by the movements of the profit rate? In this investigation we will use the model presented in section 11.5 (equations 11.9 and 11.10): ~ut

= -(1 -

~ 2 st = A~ut

u)ut-1 - est

+ B'ut + C'st-1

Coefficients u and e account for supply behaviors. Conversely, A, B 1 , and C 1, which result for the combination of several parameters of the model, only refer to the formation of demand.4 The problem is to determine which among these five parameters depends on the profit rate. We use the same method as in the previous section. For example, in order to test for the dependence on r of parameter A, we writ.e A= Ao+ Alrt, i.e., introduce in the second equation a new interaction term rt~Ut (leaving the rest of the system unaltered). For a test of the five parameters, five separate estimations must be made. The results of this investigation are presented in table 12.1. One can see that the only significant term concerns coefficient c in the decision to produce. Coefficient (1 - u ), also in the decision to produce, is second, but not significant. The best

Business Fluctuations

228

estimation is the following: tl.u1 = - 0.0950 Ut-1 - 0.234 St+ 3.68 rt St (t=6.3) (t=·B.1) (t=2.9}

fl.

2 St

=-

0.0875 fl.ut - 0.0274 Ut (t=2.6}

-

(t=2.2}

0.170

(12.4) St-1

(t=7.1)

Table 12.1 - Student's t of the interaction terms A

B'

C'

-(1 - u)

e

1.0

0.7

0.6

1.5

2.9

Thus, it appears that the primary impact of the profit rate on stability is clearly located in the decision to produce (the supply side), mostly in its effects on parameter e which measures the sensitivity of firms to the level of their inventories-and not in the demand equation. 5 Larger profit rates diminish e ( e = 0.234 3.68r) and improve stability.6

12.3 Instability as a function of the profit rate It is possible to illustrate the dependency of stability on the profit rate by computing, A( r ), the dominant eigenvalue as a function of the profit rate. (As in section 11.6, the significance of the results can be improved by considering the nonlinear character of some reactions.) For the entire period 1953-1989, the average value of A( r) is 1.01. But it is also possible to provide estimates of A for various subperiods, as shown in table 12.2. Concerning the subperiods, there is no surprise that the profile obtained is the inverted image of that of r. The 1950s appear as a period of average stability. A very significant restoration is manifested in the 1960s when the profit rate peaks at high levels. Then the 1970s stand out as a period of exceptional instability

The Impact of the Profit Rate

229

(a high plateau in the value of A) and, finally, a slight restoration is manifested in the 1980s. Table 12.2 - A measure of instability 1953-59 1960-69 1970-79 1980-89 1953-89

A(r)

1.00

0.97

1.03

1.02

1.01

12.4 Profitability, liquidity, and stability Profitability is an important determinant of stability, via. the behavior of firms, and we have shown that this relationship expresses the dependence of the adjustment to disequilibria between supply and demand in the decision to produce on r. One hypothesis in interpreting this relationship is that profitability is a crucial determinant of the liquidity of firms. When firms are illiquid, they tend to be very cautious in committing their liquid assets to production when their inventories are bloated. This is precisely what parameter e measures. Obviously it is always possible to borrow in the short term, but the firm will have to bear the costs of this debt, and the debt will mature at some point. It is possible to test this hypothesis using financial accounting data (Flow of Funds). Since data are not available for Manufacturing, we used series concerning the nonfarm nonfinancial corporate sector. The method (interaction terms) used is the same as in section 12.1. 7 A broad set of accounts have been studied, aggregated or disaggregated, for example, total-financial assets or deposits, or total short-term debt or total debt, etc. In accordance with the hypothesis above, the most significant results are obtained for various measures of liquid assets. In a rather puzzling manner, the indebtness (the fluctuations of the amounts of debt outstanding, or of

230

Business Fluctuations

ratios such as debt/ own funds) does not seem to influence supply behavior in the short term. This finding contradicts the emphasis often placed on indebtness in the analysis of business fluctuations. 12.5 A minimum profit rate?

The relationship drawn between stability and profitability suggests the existence of a kind of minimum profit rate. If the profit rate is too low: then the economy will be unsiable, i.e., taken into unusually frequent and large fluctuations. We consider this limitation to be a crucial feature of capitalism. Once the notion has been recognized, it is, however, also ~mportant to keep in mind a number of important provisos: 1. The profit. rate which affects the behavior of firms is not only determined by the movements of wages and technology, but also by numerous "institutional" mechanisms-such as taxes, interests, and dividends payments. 2. Stability is a function of profitability, via its impact on the suppy behavior of firms. However, stability is also affected by other factors, including investment, money and credits, and policy. Again the role of institutions is prominent in these respects, in particular, monetary institutions. 3. The model presented in this book remains very simple. For example, only commodity-producing industries, with a true supply behavior, are considered. The existence of other sectors, such as services, does not question the basic principles of the model, but the growing weight of these sectors in the economy modifies the stability condition. Our analysis goes beyond the mere statement that the notion of a minimum profit rate is only relative to a given institutional environment. As we will contend

The Impact of the Pront Rate

231

in chapter 18 (cf. the tendential instability thesis), this environment is periodically transformed as a response to the actual manifestations of instability. The inferior tolerable boundary of t.he profit rate can be moved downward if the institutional environment (monetary institutions and policies, in particular) evolves favorably.

NOTES 1.

2. 3. 4.

5.

6. 7.

The problem is well posed by Duncan Foley: "If the rate of profit were indeed falling consistently, why would the capitalist system not adapt to this fall through a gradual reduction of the rate of accumulation? [...] this explanation of crisis [by a diminished profit rate] has to produce some systematic reason why a fall in the rate of profit leads at certain moments to sharp and discontinuous adjustments in economic activity." (Foley D. 1986(a), p.153). This approach to the impact of profitability is now gaining acceptance in Marxist and Keynesian literature where the use of dynamic models is becoming popular (for example, Shaikh A. 1986 and Bowles S., Boyer R. 1990). The profit rate has been normalized subtracting its average and dividing by its standard deviation. Various interest rates have been tested, more directly related to firms or final consumers, for the short and long terms. This relationship to demand is either direct for b and c in the demand function, mediated by the issuance of money for d and e, or transmitted via the variations of prices for a and /3. Note that it is because €, and not another coefficient, is a function of r that there is no significant term in TtUt-3 in equation 12.2. Condition 11.7 implies that a diminished € is reflected in a lower e and, therefore, a lower value of A. Since the various accounts in the balance sheets of firms display historical trends, we detrend these variables, and keep their fluctuations (using the Whittaker filter).

13. Business Fluctuations other Paradigms

• In

In the first decades of the 19th century in England, industrial production began to exhibit recurrent fluctuations, with a succession of periods of acceleration and sudden collapses of output. Since then, the instability of the general level of activity has remained a permanent feature of capitalist economies. With a short exception in the 1960s, when a large segment of the economic profession thought that the progress of stabilizing policies had eliminated business fluctuations, the analysis of this inherent instability constantly puzzled economists. Rkardo had already devoted chapter 19 of his Principles (1817) to the states of distress in which the economy was periodically taken. Marx was one of the first economists to describe the modern form of the phenomenon in some detail, and to suggest interpretations. Since this heroic era of the formation of economic thinking, the number of theories has multiplied to amazing proportions. In the present st.age of economic knowledge, no consensus exists to date among economists concerning the analysis of business fluctuations.I Even focusing on one specific train of thought, the notion of "Marxist crisis theory," for example, encompasses a very large set of analyses, whose contours and internal structure are already very difficult to delineate. The present chapter does not purport to do justice to this wealth of contributions. Our ambition is limited here to a short discussion of two perspectives, neoclassi232

Other Paradigms

233

cal and Keynesian, to be compared to the interpretation given in the previous chapters. However, as in the case of Marxist economics, the reference to these two schools is certainly not precise enough to point to well-defined analytical schemes. We will consider successively two opposite examples. We select the real business cycle theory to represent modern neoclassical, or rather newclassical, analysis, and Keynes himself for Keynesian economics.2 As a preliminary to this comparison, we will briefly recall the core propositions of these approaches. Finally, in relation to the general line of argument in this book, special attention will be paid to the role conferred to the profit rate in various analyses of crises. An appendix is devoted to a brief discussion of Richard Goodwin's model of economic fluctuations. 13.1 A comparison with new-classical and Keynesian analyses In the neoclassical train of thought, business fluctuations are explained either by "obstacles" to free competition or exogenous shocks. Real business cycle models provide a cogent example of the second point of view. At the base of these new-classical models is a general intertemporal equilibrium model, with rational expectations. This theory is denoted as real business cycle, since money does not play any role in the model. These models are stochastic, i.e., the economy is subject to recurrent shocks. A priori, exogenous shocks display the characters of a white noise without autocorrelation, i.e., the observation of the shock in one period does not provide any information concerning the shock in the next period. On the contrary, business-cycle fluctuations reveal a strong degree of autocorrelation, i.e., overheatings or recessions last more than one period. These two categories of shocks are illustrated in the diagram below (white noise in (a) and autocorrelated shocks in (b)).

Business Fluctuations

234

The purpose of the model is to show that the response of economic agents to a white noise (their intertemporal optimization) "transforms" these shocks into fluctuations, such as that observed along the phases of the business cycle . •

.. .. . . . . ..... . •. . ·. : . . : : . ..·---.-::-::. .. ... . . : ·. : '. ·. ···.. · .. .... ,i ••

:;:---.--···~.';,~""~·y·-:"-·-;-.--

·(a)

....... ... . ·...... ···... . . ' ... ·: .. "•\.

,.... ._ . ... .·. . - ·:

':t:--:·-:-..........---_r-=-:.:~-·::~~·:··-·-·--:-r.-····?

..

~·

(b)

We now turn to Keynes: analysis. It is well known that Keynes attempted, first of all, to explain the general level of activity and not to develop a theory of business fluctuations. The core of Keynes' analysis must be supplemented by his chapter 22, Notes on the Trade Cycle, in the sixth part of the book, entitled in a very telling manner Short Notes Suggested by the General Theory (Keynes J.M. 1936). The level at which economic activity will stabilize is determined by exogenous demand, i.e., basically investment. The business cycle reflects the sudden metamorphoses of the marginal efficiency of capital, a very volatile variable, strongly influenced by psychological conditions, which impacts on the decision to invest. The explanation of the transformation over time of the variance of business fluctuations is different in each analysis. By the transformation of the Yariance of business fluctuations, we mean the distinction of periods (such as 1976-1980, in figures 11.1 and 11.2), in which the amplitudes of the fluctuations of the general level of activity are small, and periods (such as 1970-1975) of recurrent switches from high to low activity. Within real business cycle models, the variance of business fluctuations is related to that of exogenous

Other Paradigms

235

shocks. The model accounts for the autocorrelation of the series, but does not explain endogenously the variation over time of the variance of the series. For Keynes this variance mirrors that of the marginal efficiency of capital, and he does not investigate the causes of these variations, considered as rather subjective.3 In our models, the variations of the variance of business fluctuations results from the variation of reaction coefficients. If these coefficients change, and, for example, the dominant eigenvalue rises, the same exogenous shocks will produce fluctuations of larger variance. 13.2 Business fluctuations and crises

A specific feature of the real business cycle is that business fluctuations are described as a manifestation of the normal course of events. At each period, intertemporal optimization "'-ith rational expectations is realized, incorporating the new information contained in the last variable observed. All the ingredients of traditional neoclassical analysis are combined there: 1. The functioning of the system is never the problem.

There is no better reaction to the new situation. 2. The economy is always in an equilibrium. (Only voluntary unemployment may prevail.) 3. State intervention (in particular, with respect to the management of money) is, at best, neutral, or detrimental. Of course, neoclassical economists know that the actual economy does not always function as described by the model. But the basic recommendations suggest that all impediments to its "normal" functioning should be lifted, and laissez-faire should prevail. Along such lines, the concept of crisis is irrelevant. Business fluctuations do not manifest a disruption in the normal course of the economy. An important difference between this analysis and

236

Business Fluctuations

that of Keynes hinges on this notion of the normal course of the economy. Following Keynes, the economy has only a limited ability to function on its own. Individual selfinterest does not solve all problems (does not correct optimally for all shocks and does not guarantee the "normal" utilization of resources), and the assistance of the state is constantly required. Our models describe situations in which the system does not always function properly, and the notion of crisis is crucial. The reactions to disequilibrium of individual agents (even "optimal" reaction) do not guarantee stability in dimension. When stability conditions are not met, dramatic movements are generated, which are not the optimal corrections of disequilibrium, but the wandering of an economy out of control. vVe share this point of view with the Keynesians, but we are less optimistic concerning the ability of an "optimal policy" to eliminate business fluctuations, since instability is constantly recreated in the system, in spite of the progress of stabilizing devices (see section 18.4).

13.3 The role of the profit rate The profit rate is ignored in real business cycle analysis, but it is often central to Keynesian and some Marxist (or Marxist tinged with Keynesianism) crisis theories. Here two schools of thought must be distinguished. Both refer to the occurrence of crises in relation to the deficiency of demand: an. excess profitability leads to a lack of demand for consumption goods, and a de:fi.cient profitability leads to a lack of demand for investment goods. Even if we share with these analyses the view that the profit rate is an important variable, our interpretation differs considerably. In the analysis of stability in dimension, we emphasize the influence of the profit rate on supply behaviors, instead of demand. The view that crises arise from a deficient demand for consumption goods (underconsumption), in relation

Other Paradigms

237

to the excessive profitability of capital, has always been a popular interpretation of business fluctuations. In the 1930s, it was denoted as the man-on-the-street interpretation of the Great Depression. It was given a theoretical foundation at the Brookings Institution, in particular, by the work of Harold Moult.on (1935). It is also a common explanation in the Marxist literature (cf., for example, Baran P., Sweezy P. 1966).4 This analysis of the Great Depression has been revived in France by the Regulation School (Aglietta M. 1979, Boyer R., Mistral J. 1978, and Lipietz A. 1979), which describes the 1920s as a period of intensive accumulation without mass consumption. Intensive accumulation is characterized by a rapid growth in the productivity of labor. The lack of mass consumption accompanies the high levels of profitability. Deficient demand for consumption goods, combined with increased supply, was responsible for the depression. Since the argument hinges on the formation of demand in relation to income distribution, the crucial variable here is not the profit rate but the share of profit in the product. · Taking this interpretation of crises at face value, the expectation is that the profit share increases before the occurrence of crises. In particular, this should be the case for the Great Depression to which this analysis has been primarily applied. It is easy to test for the factual relevance of this analysis. The share of gross profit in GNP is, to say the least, not exceptionally large or increasing in the 1920s (see figure 13.1).5 The share of consumption is not exceptionally low either.6 These observations provide, in our opinion, a powerful indictment of the underconsumptionist argument. The profit share (net or gross) has been basically constant historically and its short-term variations reB.ect, and do not explain, business-cycle fluctuations. Another traditional interpretation of the importance of profitability is the idea that the profit rate moti-

Business Fluctuations

238

The share of gross profit in GNP (18691989)

Figure 13.1 Profit share

0.60 0.50 0.40 0.30 0.20 0.10 0.00-+-~~....-~--.,.-~--.-~~--.-~~....-~~...-~--.

1860

1880

1900

1920

1940

1960

1980

Year

vates investment. Capitalists invest because they are attracted by a return on their investment that they judge sufficient. Thus, a large profit rate induces a large output. In one guise or another, this analysis is common in the literature. It was at the center of Keynes's theory of investment (the comparison between the marginal efficiency of capital, that is an expected profit rate, and the rate of interest): Now it is obvious that the actual rate of current investment will be pushed to the point where there is no longer any class of capital-asset of which the marginal efficiency exceeds the current rate of interest. (Keynes J.M. 1936, Ch.11, p.136)

Although they lead to opposite conclusions, these two views of the importance of profitability are not mutually exclusive and they can be combined. Following this interpretation, capitalist economies confront a permanent dilemma, and constantly oscillate between a deficient demand for consumption and investment goods. The

Other Paradigms

239

point is to find the profit rate which maximizes output, or at least, a tolerable range of variation of the profit rate.7 We do not consider these analyses as relevant, because, in particular, they thoroughly ignore the role played by money and credit in the determination of equilibrium (cl section 11.9).8

NOTES 1.

2.

3.

4. 5.

6. 7.

A synthesis of the major trains of thought, which illustrates strikingly the broad variety of hypotheses, can be found in Zarnowitz's 1985 study. New Keynesians do not have much to say concerning business fluctuations, since most of their efforts are devoted to the explanation of the rigidity of prices. The nature of expectations in the two perspectives is also different, rational for neoclassicals, and "psychological" for Keynes. In our opinion, expectations play a secondary role. See also Devine J. (1983). Since the issue is that of demand, the consideration of the share of gross profit in the GNP seems more adequate than the share of net profit in NNP, but the two shares are very similar. See Dumenil G., Levy D. {1989(b)), figure 3. These analyses can be stated very simply in a Keynesian framework. The equality between the product and demand can be written Y =I +C, with an obvious notation. C is proportional to the product: C = cY. The underconsumptionist thesis implies that c is a decreasing function of the profit rate. Thus, the product itself is a diminishing function of r, Y = 1/(1-c(r)), and the rise of the profit rate carries with it realization problems. The second view, concerning deficient investment, can be stated in the same formalism. Investment is an increasing function of the profit rate I I(r). Thus, the product is an increasing function of r: Y = J(r)/(1- c). Combining the two mechanisms, one has Y = J(r)/(1-c(r)),

=

240

8.

Business Fluctuations in which it is possible to determine the value of 7' which maximizes Y. We also disagree with the importance conferred on sectoral maladjustment in the explanation of crises. This interpretation fully contradicts our thesis concerning the stability in proportions of capitalism.

Other Paradigms

241

APPENDIX 13.Al Long-term cycles and the pro:fi.t rate The profit rate is also central in the model of fluctuations developed by Richard Goodwin (1967). The overall idea is simple. Accumulation leads to the rise of employment (at diffe.rent degrees depending on the intensity and forms of technological change). The rising employment stimulates the progress of real wages. Consequently, the profit rate falls. Since accumulation is a. function of the profit rate, the declining profitability results in a diminished rate of accumulation. This movement puts a check to the rising movement of wages, a development which is favorable to the profit rate, and the same chain is repeated. Note that, with this model, lower wages are favorable to a faster growth of employment and vice versa. Cycles are generated, which account for a succession of periods in which the growth rate of the economy is alternatively large and small (independently of business fluctuations). It is well known that the model is not structurally stable. This is equivalent to saying that the cycles obtained by Goodwin may disappear if the form of the model is only slightly modified. We treat this model in an appendix, since it does not concern business fluctuations in the traditional sense, as those considered above, but some kind of longer-term fluctuations related to the changing pace of accumulation (what we call long-term dimension). Even if one agrees with the view that the profit rate is a determinant of accumulation (cf. chapter 16), it is not clear that this model is empirically important in the explanation of unemployment, and it does not carry any insighi into the nature of short-term business fluctuations. Note parenthetically that there is a similarity between Goodwin's analysis and that of Nicholas Kaldor (1957). In Kaldor's model full employment is ensured if the profit rate is fixed at the appropriate level. The growth rate of the economy, p, must be equal to the exogenous growth rate of labor n. This rate is the product of the profit rate, r, and the propensity to save of capitalists, or rate of accumulation, a: p =or. A balanced growth path is reached if r n/o, and the value of the wage rate is correlatively determined, since the profit rate is a function of the wage rate. No cycles are observed in Kaldor's model.

=

PARTY TECHNOLOGY AND DISTRIBUTION: A HISTORICAL PERSPECTIVE

14. The Historical Profile of the Profit Rate The analysis of the historical profile of technology and distribution is not a major subject of contemporary economics. To our knowledge, little contemporary research can compare to the pioneering works of Simon Kuznets, Raymond Goldsmith, John Kendrick, or Stanley Lebergott, in the 1950s and 1960s.l The mainstream is content with an overview of "stylized facts":2 wages and labor productivity have been growing historically, and the productivity of capital and the rate of profit have no historical trend. Historical analysis is also not a major concern of Keynesian analysis. With the important exception of heterodox economists' interest in broad historical syntheses and, in particular, Marxist economists testing for the relevance of Marx's analysis of the tendency for the profit rate to fall, 3 the broad vision of capitalism as a mode of production with a number of inner tendencies, familiar to the three classical economists, Smith, Ricardo, and Marx, is no longer a major focus of investigation. This fifth part of our study is an attempt to contribute to this older debate. The point of view adopted here is specific in that historical tendencies are considered globally, as a network of interrelations among the major aggregate variables, wages, the productivities oflabor and capital, the capital-labor ratio and, of course, the profit rate. In this investigation of historical tendencies, we separate between the relative values of the variables, some form of "proportions" -like the two productivities which relate each input to output, or the capital-labor ratio245

246

Technology and Distribution

and their absolute levels, some form of "dimension" like the capital stock, output, and employment. The perspective of "proportions" is adopted in the first two chapters, in which distribution and technology are considered. The third chapter, devoted to accumulation and growth, deals with "dimension" phenomena. In the analysis of their trends and reciprocal relationships, the above variables will be considered in very crude definitions: 1. Profit is measured as total net product minus labor

income, and capital is reduced to its fixed component. 2. All categories oflabor are aggregated together in spite of important differences in their functions within the firm. This is due partly to the lack of data, as well as to the desire to simplify the description. 3. There will be no distinction made between various sectors of the economy. Thus, the purpose of this part is to draw with broad strokes the picture of the major tendencies in the US economy since the Civil War. Only the last chapter of this part should be viewed as an exception to this general approach. There, we analyze the profile of the profit rate, over shorter time periods, taking account of a number of institutional distinctions, such as taxation and financial assets, thus adding much complexity to the previous picture. The present chapter is primarily descriptive. Moving backward in time, we reconstruct the historical movement of the profit rate since 1869. A major transformation of trend in this profile, observable in the middle of this 121-year period, provides the basis for the distinction of three successive stages, which, we believe, is crucial in the understanding of the evolution of the US economy. The series used in this part to describe the historical profiles of technology and distribution are presented at the end of this volume.4

The Historical Profile of the Profit Rate Figure 14.1

247

The postwar decline of the profit rate and its trend (1946-1989)

r 0.50

0.40

0.30

.

......•...

~:;--'\:..-:"-~~-. ,. . t•:.~:::/~. . t ....•...~--~-\~·.•·!'.~~-:·•·;:•:····

•.•

..... •.• ········•:t····· ······........ ········

0.20

0.10

0.00-+---.---.---.---.---.---.---.----.----.

1945 1950 1955 1960 1965 1970 1975 1980 1985 Year

14.1 The postwar decline

The movement of the profit rate since World War II has been the object of much investigation. The profile observed for this period, with the definition introduced above, is displayed in figure 14.1. The trend suggested by a dotted line, clearly sets out the contours of the decline of the profit rate in the second half of the period. 5 After World War II, up until the late 1960s, economists were familiar ·with the short-term fluctuations of the profit rate (or share of profit) inasmuch as they represent business fluctuations around a horizontal trend. In the late 1960s, they became puzzled by the possible deviation from this trend. The existence of a decline became unquestionable by the 1970s and initiated an important debate. 6

248

Technology and Distribution

Figure 14.2

The World-War-II leap forward of the profit rate for the total economy (•) and the corporate sector (o) (1900-1989)

,. 0.50

0.40

0.30

0.20 0.10 0.00--........- - . - -..........---.----.-----.--..---~----. 1900 1910 1920 1930 1940 1950 1960 1970 1980 YeaJ"

14.2 The World-War-II leap forward The literature devoted to the decline of the profit rate in the 1960s or 1970s assumed that the point of departure in the late 1940s, which is used as reference to argue that profitability has fallen, was not exceptional. Using data stretching back to the turn of the century, however, it becomes obvious that this is not the case. The levels of profitability reached just after World War II are extraordinary in comparison to both the 1920s and the earv 20th century, as is clearly apparent in figure 14.2

(•). The results of an estimation of this sudden rise of the profit rate are represented in this figure.8 A leap of 15.8 percent is observed-compared with an average value of 29.0 percent for the entire period. (One can

The Historical Profi.le of the Profi.t Rate

249

also notice that, independent of the leap, a slight trend downward in r is observed.) When viewed from the long-term perspective of figure 14.2, the rise of the profit rate during World War II unquestionably appears as an exceptional event, a restoration of major historical significance, which we denote as the "leap forward" of World War II, and represents an intriguing challenge to any student of economic historical trends. A first and quite natural reaction to the observation of the leap forward is to question the reliability of the data series and computations. Obviously, the determination of the secular profile of the profit rate requires the splicing together of several series derived from various historical studies, and the leap may only represent a deficiency in the construction of the series. It is important to underst.and in this respect that, beginning in 1929, the profit rate is constructed exclusively with BEA data. It is difficult. to appraise the prewar (and predepression) "normal" levels on the flimsy basis of a single year. However, considering 1929 alone, the leap appears in the BEA data. If there is a bias in the data, it must be found there. A second reaction to the observation of the leap is to contend that it might be due to the specific definition of the profit rate. Beginning in 1929, however, it is possible to use various measures of the stock of capital (gross capital, net capital, net capital plus inventories), and to change the definitions of profit (without correcting for the wage equivalent of self-employed persons, or without interests). It is also possible to eliminate some of the dubious components of income (such as rental income of persons) and restrict the unit of analysis to the sum of the corporate sector and sole proprietors and partners, or to the corporate sector alone, without affecting the conclusions. Abstracting from the effects of taxation which will be discussed in chapter 17, the leap forward survives any change in profi.t rate defi.nition.

250

Technology and Distribution

This robustness of the leap to changes in profit rate definitions is demonstrated in figure 14.2 ( o ), which presents a measure of the profit rate for the corporate sector, between 1929 and 1989, with a strict definition of profit, and a broad definition of capital including residential capital. (These differences explain why the general level of the profit rate in this definition is lower.) The same sudden increase is observed. 14.3 From the leap to a progressive transition

By relying more and more heavily upon historical studies, it is possible to extend the investigation of profitabilit.y trends backward in time to the Civil War. The results of this estimation are presented in figure 14.3. A straightforward examination of figure 14.3 ( •) reveals the existence of another break in the 1880s, of a similar degree to the rise during World War II, but in the opposite direction. Thus, a cursory examination of this figure would suggest the distinction of three periods: (1) From 1869 to the early 1880s, a sharp trend upward, (2) A long plateau from 1885 to 1939, and (3) A decline following World War II. Between these periods, the transitions appear sudden: a fall from 38.3 percent in 1883 to 24.2 percent, the average value of the 1885-1929 plateau, then a leap to 34.3 percent, the average value in the 1950s. On inspection, however, it turns out that this interpretation is misleading, since it ignores the important effects of business fluctuations and sudden variations in prices, which are responsible for a large fraction of the movements around basic trends. Figure 14.4 charts a proxy capacity utilization rate defined as the fluctuation of GNP around its trend (i.e., the difference between the logarithm of real GNP and its trend). By comparing the two series in figures 14.3 and 14.4, we can infer that the most dramatic impact of the capacity utilization rate would affect: (1) The high points around 1880 (a peak in the activity related to

The Historical Profi.le of the Profi.t Rate Figure 14.3

251

The historical profi.le of the profi.t rate (•) and its trend () (1869-1989)

r

0.50

..

~

0.40

••

. •

: :

..• .:~~. ~.. :-

:··!:~.....' ~.~·.··...

0.30

4 I

4': ~....

......

. .. fllii··· '-

II'.

'!t~··.....

i...'

···~...

,

,.

~:'115~• • • ~~ •; ,,./ j /'.•

~;·: : ii • ~ ~Ji: ~ ~i; ~-.;J'' :

. :.

•-;'·='

0.20

!'ii

11:. : :,J-.........~·"•~

-~·. 1....--' ....

!~:

.... ...

~'!' .....

:'

•

. , .~=" . '; :• I

6 .

:~

:~

0.10 O.OO-+-~~..--~----,.--~--,.~~--.-~~--.-~~....-~---.

1860

1880

1900

1920

1940

1960

1980

Year

Figure 14.4 Proxy capacity utilization rate (18691989) u

0.30 0.20 0.10 0.00 -0.10

..

f

-0.20

:

-0.30

'!':~

:•

~~

~tI

-0.40

-0.50-+-~~..--~----,.--~--,.~~--.-~~--.-~~....-~--,

1860

1880

1900

1920

1940

1960

1980

Year

.252

Technology a.nd Distribution

the railroad boom), (2) The low points around 1890 (a lengthy period of stagnating growth, sometimes denoted as the depression of the nineties9), (3) The fall into the Great Depression, ( 4) The sudden rise during World '\Var II reflecting the hectic activity during the war, and (5) The 1960s bulge which coincides with the rise of the capacity utilization rate in the first half of the 1960s, followed by the declining trend of the profit rate. The consideration of the capacity utilization rate is, in fact, illuminating. The World-War-II leap forward must be interpreted as the combination of two equally dramatic, but quite distinct movements: 1. An upward swing in the trend of the profit rate

(cf. figure 14.3), a result of the slow transformations of technology and of the trend of wages (see appendix 14.Al). This phase stretches from World War I to the aftermath of World War II. It reflects a spectacular transformation of technology, but this movement required some 40 years to complete, and should not be characterized as a "leap." 2. An exceptionally large fluctuation in the capacity utilization rate corresponding to the Great Depression and World War II, as clearly evident in figure 14.4.

All sharp fluctuations in the profit rate cannot be attributed to the variations of the capacity utilization rate, however. Although technology itself does not change suddenly, wages may be subject to rapid variations. This is, for example, the case for the fluctuation observed in the late 19th century which combines some business fluctuations, with the sudden variation of the labor cost (cf. figure 14.5). From 1869 to 1880, the real wage remained approximately constant, and an upsurge can be observed in the movement of the profit rate. From 1880 to 1885 the wage rate caught up quickly (by a total of 27 percent) and the profit rate fell dramatically.

Tbe Historical Profile of tbe Profit Rate Figure 14.5

253

Labor cost and its liistorical trend (18691989)

w

15.0

.•

/.

I

10.0

....r/'··'

5.0

/

.

··"

...-/'~

./·

2.0 1.5

.........•,-

.

..-;.,.~

3.0

.-:/'" Al ~11/j

'71. ·

1.0-t-----r----r---.......------.----.----.----. 1860 1880 1900 1920 1940 1960 1980 Year

14.4 A wave of technical progress

Figure 14.6 ( •) plots the historical profile of the productivity of capital (the ratio of NNP to the net capital stock, both measured in current dollars). This figure strikingly illustrates the dramatic transformation of technology which occurred between the 1920s and 1950s. Thus, the upward swing in the movement of the profit rate appears, unmistakenly, as the manifestation of an unusual wave of technical progress.10 Changes in prices are not the explanation of the leap: 1. Concerning the price of fixed capital, an examination of the second series (a) in figure 14.6 reveals that the explanation of the leap cannot be found there. This series represents a measure of the productivity of capital in which both the product and the capital stock are expressed in constant dollars. With this measure, the leap is even larger. Actually, the variation in prices

254

Technology and Distribution

Figure 14.6

The productivity of capital (1869-1989): current (•) and constant (o) dollar ratios

Px 1.5 I

.•

1.2 1.0

0.8

0.6 0.5

~

0.4~1~~~~~~~~~~~~~~~~~~~~---.

1860

1880

Figure 14.7

1900

1920

1940

Year

.

t

..

4:

••:

0

0.40

1980

The rate of return on investment (o ), the profit rate on the capital stock (•) and its trend () (1869-1989)

r

0.50

1960

•

:

0.30 0.20

"

0.10

0.00-t-~~~~-..,~~-.-~~--r-~~-.-~~..--~----.

1860

1880

1900

1920

1940

1960

1980

Year

The Historical Profile of ·the Profit Rate

255

diminished the amplitude of the movement. observed in the real values. 2. It is also clear that the rise of the profit rate cannot be attributed to the decline in wages, since labor cost rose steadily during those years, at a rate greater than the average (see figure 14.5).

14.5 The rate of return on investment (RRI) The profit rate displayed in figure 14.3 is actually a rate of profit on the stock of capital outstanding in one year, and not a rate of return which accounts for the ability of an investment made in one year to yield profit during its entire service life, following the distinction introduced in chapter 2. Recall that the RRI is the discount rate which equalizes the value of the investment with the present value of the sequence of returns (profit gross of depreciation) which results from the investment. For its computation, it is necessary to determine the technology embodied in each new vintage of investment, denoted as the vintage technology, as opposed to the average technology. The procedure used here is briefly sketched in appendix 14.A2. The results of an estimation of the RRI are displayed in figure 14. 7 ( o). The profile obtained is that of a broad oscillation. For comparison, the accounting profit rate has also been displayed in figure 14.7 (with its trend). A difference between the RRI and the accounting profit rate is that the latter is subject to business fluctuations, whereas the RRI is not. With this qualification, the two rates reveal a similar historical profile. The trend of the accounting profit rate replicates that of the RRI, with an average lag of about 10 years.

256

Technology and Distribution

14.6 Three stages in the historical profile of the profit rate and technology From the investigation in the previous sections, it follows that the profile of the underlying trend of the profit rate can be best described as a succession of three periods: downward/ upward/ downward, instead of two downward trends interrupted by a kind of land slide, as suggested by the notion of "leap" (as in :figure 14.2). This same pattern is observed for the productivity of capital, and represents very important economic transformations. We will therefore contend that the evolution of capitalism over a period of more than a century considered in this book must be perioclizedfrom the point of view of technology and distribution -into three stages. Considering the trend of the accounting profit rate, the periodization can be stated as follows. A :first period is evident from the beginning of the series up to the 1900s. At this point the tendency is reversed, and the profit rate is progressively augmented from the 1910s to the 1940s. Then, the new decline is initiated. This trend begins in 1869 at 39.3 percent, falls to the minimum value of 22.5 percent in 1912; it reaches its maximum in 1951 at 35.5 percent, and then falls back to 25.4 percent in 1989.11 The consideration of the RRl does not change this periodization, except that the turning points are about 10 years earlier, and that the recovery in the intermediate period is slightly steeper. It is difficult to determine which measure of the profit rate is superior, and the definition of three broad periods appears to be correct, even if the choice of precise turning points remains in question. The :first transition occurs around the turn of the century and early 20th century, and the second around World War II and the 1950s. This difficulty to exactly pinpoint the benchmark years does not alter the dramatic character of the transformation of the trends from one period to the next.

The Historical Profile of the Profit Rate

257

NOTES In spite of a number of notable exceptions, such as Nathan Balke and Robert Gordon, Robert Gallman, and Angus Maddison. 2. See, for example, Kendrick J .W., Sato R. (1963) and Solow R.M. (1970). 3. One must mention here the two pioneering contributions: Gillman J. (1958) and Mage S. (1963). 4. The sources and construction of the data are described in Dumenil G., Levy D. (1991(a)). 5. We use the Whittaker filter (see appendix ll.A3). 6. See, e.g., Okun A., Perry G. (1970), Nordhaus W. (1974), Feldstein M., Summers L. (1977), Lovell M. (1978), and Wolff E. (1979). 7. We devoted several papers to the discussion of this break: Dumenil G., Glick M., Rangel J. (1987), and Dumenil G., Glick M., Levy D. (1990 and 1992). The existence of a dramatic increase of profitability during World War II has not gone totally unnoticed. For example, in the 1960s, a debate developed around this issue, for manufacturing industries (Krzyzaniak M., Musgrave R.A. 1963 and Gordon R. 1967). More recently, one can find reference to the transformations which occurred during World War II in Blanchard 0., Fisher S. (1989) (figure 1.3, p. 4, and note 6, p. 30). Nevertheless, this aspect of US economic history remained unduly neglected and, in our opinion, was never interpreted correctly. 8. Vile fit a linear trend line to the series, imposing a same slope before and after the break and a dummy variable: 1't = a + bt + cDt + 7/t· Di is equal to 0 prior to the transition year, and 1 subsequently. The size of the leap is measured by the value of c. 9. See, for example, Hoffman C. (1970). 10. For Robert Gordon (1967) the restoration of the profit rate is the effect of a true metamorphosis of technology, viz. a rise in the productivity of capital, as we believe is correct. But, he does not provide any explanation for its sudden character. 11. In spite of important differences in the two approaches, since Angus Maddison ( 1991) never considers variables such as la-

1.

258

Technology and Distribution bor cost or the profit rate, and begins his investigation earlier, one can notice the similarity between our periodization and his: 1820-1913, 1913-1950, 1950-1973, and 1973 onwards (p. 85 ). It is too early, in our opinion, to be assertive concerning the existence of a break in 1973.

The Historical Profile of the Profi.t Rate

259

APPENDICES 14.Al The logistic trend In order to test for the hypothesis of a pattern of variation in three siages and to date the transitions, we adopt the metlwdology illustrated in figure 14.8.

Figure 14.8 A pattern in three stages: entire model as in equation 14.1 (a) and logistic alone as in equation 14.2 (b)

1······················;......· · - •ma.ll 1:&. /"

I

j

,,......

"'............

/'..

l ....··

i/

,. j:. f

ltiPg• ~/

..---/~.~:..../

~

o--""-----'i (b)

(a)

As shown in panel (a), we assume that the profile of the variable considered is nearly linear in the first and third stages, with possibly different slopes. The transition is represented by a logistic curve (with t =Date - 1900):

X =(a+ bt)(l - L(t)) + (c + dt)L(t) in which

L(t) =

ezp t-'i;( 1

T

t-t) + ezp T

(14.1) (14.2)

Function L(t) alone is determined by the two parameters t and A. It increases from 0 for t -+ -oo, to +1 for t -+ oo, with any maximum slope in between (obtained fort 'i), depending on the value of A. As shown in panel (b) of figure 14.8, it can account for a slow transition (a large A) as well as for a sudden leap (a small A). Nearly half of the transition as modeled by the logistic alone is concentrated between t - l.lA and t + l.lA.

=

Technology and Distribution

260

14.A2 The determination of the vintage technology and the rate of return on investment The general procedure used to determine the vintage technology, i.e., the technology embodied in each vintage of investment, can be briefly sketched as follows: 1. The vintage technology can be characterized by its capital productivity, labor productivity, and its discard schedule associated with its average service life. 2. On the basis of the investment flow and the description of the l'intage technology, it is possible to reconstruct the average technology. 3. We choose parametric expressions for the three variables characteristic of the vintage technology, as functions of time, and the vintage technology is estimated by regressing the series describing the average technology. A first assumption is tliat the two productivities vary with time as new investments in new productive combinations are realized, but once a given technology has been adopted, its features cannot be modified: technology is putty-clay. This model certainly overstates the rigidity of technology to some extent, but gives a more realistic description of technological change than the putty-putty model implicit in most studies. A second assumption is that the productive power is measured by the gross (and not net) stock of capital. This is equivalent to saying that a building or machine can be used productively independently of its age, as long as it has not been discarded. The net stock of capital accounts for the loss of value due to the limited time spa11 in which it can still be used productively, not for its present productive power. Once the vintage technology has been determined, it is possible to compute the sequence of returns (or gross profit, i.e., the sum profit plus depreciation). The returns in period t', for one unit of fixed capital invested int is denoted 'll'(t, t'). The BEA provides an estimate of the fraction W(t, t') of an investment realized int and still in use in t'. (W(t, t') declines from 100 percent to zero when t' increases.) With p denoting the relative price of investment in comparison to GNP, the RRI, r, corresponding to an investment realized in t, is determined by the following equation:

( ) -_ pt

~ W(t, t 1 )'11'(t, t')

L.J

t'=t+l

I

(1 + r)t -t

The Historical Profile of the Profit Rate

261

Since W(t, t') is equal to 0 if t' is large in comparison to t, the series is a polynomial in 1/(1 + r), whose degree is equal to the maximum number of periods of use. The proof of the existence of a unique positive root in the above equation is straightforward, since all coefficients in the polynomial are positive. From this, the existence and uniqueness of a RRI greater than -1 both follow. A more explicit account can be found in Dumenil G., Levy D. (1990(c)), where this method is applied to Manufacturing.

15. Historical Tendencies In the preceding chapter, emphasis was placed on the profit rate, and its historical profile. It was shown that a strong similarity exists between the movements of the profit rate and those of the productivity of capital. The purpose of the present chapter is to analyze the profit rate as a component of a broader network of reciprocal relations, including the dynamics of technology and wages (or labor cost ).1 The literature frequently discusses one aspect of these relationships, in line with the perspective adopted in the previous chapter, going from technology and labor cost to the profit rate. Thus, it is the "origins," "causes," or "factors" of the variations of the profit rate which are discussed. For example, the investigation may attribute a falling profit rate to a rising labor cost or increasing technical composition of capital, when the explanation may be more complex. We believe that this point of view arbitrarily singles out the profit rate as the object being determined, and ignores the general interplay among these variables, for example, the feedback of the profit rate on the evolution of technology or wages. This unilateral approach is in direct contradiction with the overall demonstration in this book which stresses the effects of the profit rate on the economy. Thus, this chapter considers the profit rate for what it is in our opinion, viz., a variable in a system, which is determined by and simultaneously affects other variables. It. emphasizes two major impacts of the profit rate, its function in the selection of technical innovations 262

Historical Tendencies

263

and, thus, its influence on the historical tendencies of technology, and its impact on the movement of wages, whose progress is subject to the levels and variations of the profit rate. Once the definitions and framework of analysis have been introduced, the chapter will deal successively with distribution (labor cost and the profit rate) and technological change. A dynamic model is presented and then estimated (see Dumenil G., Levy D. 1992(f))

15.1 Definition of the variables Four variables are considered in this analysis: labor productivity and the capital-labor ratio for technology, and labor cost and the profit rate for distribution. It is important to notice that two variables are required in order to describe technology, since two inputs are at issue, labor and fixed capital. Technological change is not reducible to the movement of labor productivity. (The productivity of capital, as in figure 14.6, is equal to labor productivity divided by the capital-labor ratio.) The definitions of these variables are straightforward. Labor productivity, Y / L, is the ratio of the Net National Product (NNP) in constant dollars, Y, to the number of hours worked by employees and self-employed persons, L. Labor cost, w, is defined as the nominal hourly wage deflated by the NNP deflator.2 Note that the capital-labor ratio, K / L, is the ratio of the net stock of fixed capital, K, deflated by the NNP defiator for consistency with the expression of the profit rate below, and the number of hours worked. It measures the degree of mechanization in the economy. The capital stock includes structures and equipment and is net of depreciation. The four variables above are linked by the definition of the profit rate (cf. equation 2.1) and, consequently, are not independent.

Technology and Distribution

264

15.2 Historical trends and fluctuations: the pattern in three stages In describing the historical profile of a variable, we distinguish two components, its historical trend and its historical fluctuation. Consider, for example, labor cost as plotted in figure 14.5. A clear upward trend is evident in this figure. The average annual growth rate is equal to 1.95 percent. We denote this linear trend over the entire period as the historical trend of this variable. In a first period the growth rate is smaller than its historical average, then it becomes larger, and eventually returns to lower levels ( 1.47, 2.32, and 1.53 percent respectively). As a result, the series describes a large fluctuation around its historical trend, which we denote as its historical :Buctuation. Table 15.1 - Average annual growth rates* 1869-1912

1912-1951

1951-1989

1869-1989

w

1.47

2.32

1.53

1.95

Y/L K/L

1.22

2.32

1.52

1.94

2.06

0.29

2.19

1.45

r

-1.60

1.44

-0.84

0.09

Y/K

-1.15

1.45

-0.82

0.09

*Percentage points

The same configuration can be observed for labor productivity with a clear upward historical trend and a similar historical fluctuation reflecting the same configuration slower/ faster/ slower. This pattern is also evident for the capital-labor ratio, but the succession of the three phases of its hist.orical fluctuation is the symmetrical of the above faster/ slower/ faster. (These two series are plotted in figures 15.2 and 15.3.) As shown in the previous chapter, this same picture is even more

Historical Tendencies

265

obvious in the profiles of the profit rate and productivity of capital (see figures 14.3 and 14.6), since the slopes of their historical trends are very small. Table 15.1 displays the values of the growth rate of the variables for the three subperiods determined in the preceding chapter and the entire period. Thus, it appears that the three periods identified in the previous chapter for the profit rate, last decades of the 19th century, first half of the 20th century, and since World War II, are evident in the historical fluctuations of all variables. 15.3 Basic relationships

The rest of this chapter is devoted to the analysis of this similarity in the historical fluctuations of the variables, which should not be mistaken for coincidence. This similarity actually echoes the system of reciprocal relationships which links technology and distribution. To the accounting derivation of the profit rate one must add two important feedbacks of the profit rate on technology and wages, as shown in the diagram below. (2)

Tech.~

(1)

Accounting derivation

~·

(2)

Impact of the profit rate on technology

(3)

Impact of the profit rate on wages

w~

The profit rate definition (1 ), which already links the four variables, will be combined with three other relationships to provide a complete dynamic model of the four variables. These three additional equations express very fundamental economic mechanisms: 1. Within technology itself, the progress of labor pro-

266

Technology and Distribution

ductivity is governed by the increased mechanization of production, i.e., the rise of the capital-labor ratio (capital deepening). 2. This capital deepening is a consequence of the rise of labor cost, via the profit rate (1 and 2). 3. The rise of labor cost (3) is, in turn, conditioned by the movement of the profit rate. It is important to stress initially that these three relationships do not account for the entire spectrum of dynamics of a capitalist economy, which are obviously more complicated and far-reaching. Quite the contrary, these tendencies should be interpreted in their interplay with a vast array of technical, organizational, social, and political events. Consider, for example, the third relationship which subjects the progress of the labor cost to the profile of the profit rate. That labor cost and the profit rate may be linked in a given analytical relationship does not preclude the relevance of class struggle in the analysis of the determination of wages. A complete analysis of wages cannot be summarized in a single equation. Rc:i.ther, this equation reveals the existence of quantitative regularities in the outcome of social conflicts between workers, motivated by the improvement of their working condiiions and living standards, on the one hand, and firm resistance to the erosion of their profit rate, on the other. In a siir...ilar manner, this analysis does not gainsay the role played by recurrent tensions on the availability of the labor force, as they may follow, for example, from the acceleration of accumulation-and the periodic alleviation of such pressures through crises or stagnating growth-but the emphasis is placed here on historical profiles, independent of the effects of shorter-term fluctuations. The same kind of interpretation must be given to the second relationship above. This relationship expresses in a very concise form the effect of labor cost on the profile of technological change. It does not ·deny the ex-

Historical Tendencies

Historical :fluctuations of tbe profit rate (•) and labor cost (o)

Figure 15.1 ln~, lnr

0.481 0.40

267

•• •

~

0.32 0.24 0.16 0.08 0.00

·-....---·~....

-0.08

•••

;.

/~••.. . ·-----·----·;,&..... •

·.•••" - . , / ·;

-0.16

-0.24-+---.----~-""-.....---..-1- - -..........--.-------.

1860

1880

1900

1920

1940

1960

1980

Year

planatory power of competition among individual firms, which is a strong stimulus to innovation, or the transformations of relations of production which condition the progress of technology, within and outside firms. As in the case of the wage-profit rate relationship, the equation at issue here summarizes a large web of individual behaviors and social relations which account for a particular historical regularity (for which we provide an ex post measurement). Other types of relationships have also been excluded, because they lack true historical relevance. For example, we do not consider the induction of technological change by the growth of output (the so-called Kaldor-Verdoorn Law3), and do not include demand into the historical dynamics of the system. 15.4 Labor cost and the profit rate

We begin the analysis with the last listed relation, which

268

Technology and Distribution

links labor cost and the profit rate. It is popular to connect the determination of wages (or labor cost) to labor productivity. This "pegging" of wages to labor productivity is based on the view that the profit share must remain more or less constant historically. This view is mistaken.4 The crucial variable for capital is the profit rate, not the profit share. The profit share is relevant only inasmuch as it affects the profit rate. Profitability must be kept under control to some extent. Diminishing (or low) profit rates will increase firms' resistance to rising labor costs, and conversely for increasing (or high) profit rates. Low profit rates lead to recurrent recessions (cf. section 12.5) and the slowing of accumulation, and create unfavorable conditions for the growth of labor cost. The historical relationship between the growth of labor cost and the movements of the profit rate is apparent at the level of the historical fluctuations of the two variables: Historical Historical :fluctuation of r :fluctuation of w ~

We already noticed that the comparatively smaller slopes of the labor-cost curve in the first and third stages of our periodization coincided with a diminishing profit rate, whereas the acceleration of labor cost was associated with the restoration of the profit rate in the intermediate stage (cf. table 15.1 and figures 15.4 and 15.5). The link between the two variables is actually complicated and merits more careful examination (see appendices 15.Al and 15.A2). It depends on the time frame in which it is considered: short term, long term, very long term (historical fluctuation and historical trend). The investigation here is confined solely to the very long term. The historical fluctuations of w and r (as determined

Historical Tendencies

269

in appendix 15.Al) have been plotted in figure 15.1. A positive correlation is revealed, with a large correlation coefficient (of 89 percent). It illustrates the view introduced above that the declining profit rate during the first stage of our periodization was associated with a low (smaller than its historical average) growth rate of labor cost, and that the same kind of configuration was observed during the third stage. Conversely, during the second stage, the restoration of the profit rate was paralleled by a growth rate of labor cost greater than its historical average. The historical relationship (historical trend and historical fluctuation) between labor cost and the profit rate can thus be modeled as: lnw = e +ft+ glnr

or

p(w) =

f + gp(r)

(15.1)

In the first equation, e+ ft represents the historical trend of w, and g ln r accounts for the relationship between the two historical fluctuations. Using the notation p(x) to denote the growth rate of x, this relationship can also be expressed as in the second equation. A more careful examination of figure 15.1 reveals, however, that the historical fluctuation of w lags by about five years with respect to that of r. Our interpretation is that the variation oflabor cost is simultaneously conditioned by the variation of the profit rate and its absolute level. In the early 20th century, for example, the low levels of the profit rate prolong the fluct.uation downward of labor cost, whereas the profit rate is already increasing. In a similar manner, the high levels of the profit rate in the 1950s and the first half of the 1960s extend the beneficial effect of the rise of the profit rate on the labor cost into the subsequent years when the profit rate is already declining. Thus, we will add the value of the profit rate (its logarithm) to the variables in equation 15.1 expressed

270

Technology and Distribution

in terms of growth rates:

p(w)

= f + gp(r) + hlnr

(15.2)

15.5 Technological change

We now turn to a description of technological change and the modeling of the two first relationships introduced in section 15.3. We approach technological change with an evolutionary "mood" (see Dumenil G., Levy D. 1992( d)): 1. Firms do not. have a global scan of technological alternatives. At each period new techniques appear randomly, as the unpredictable outcome of R&D activity (innovation is a random process). 2. Innovation is assumed to be neutral (i.e., neither labor- nor capital-saving). _ 3. Firms adopt new techniques whenever they yield a profit rate larger than those in use at going prices. Since the profit rate is a function of labor cost, the historical (upward) trend of the labor cost imparts a bias to technological change toward the more extensive use of capital. Ex post, tecfo10logy (labor productivity and the capital-labor ratio) appears to be a. function of the labor cost w. If the pace of innovation were steady (assuming a constant rythm in the apparition of new techniques), stable5 historical laws, or historical tendencies, would be obtained, such as:

lnK/L =a+ blnw lnY/L = c+ dlnw

(15.3) (15.4)

Note that these two equations also imply that labor productivity can be expressed as a function of the capital-

Historical Tendencies

271

labor ratio, as is traditional:

= A+ B ln K / L da A=c- and B=~ b

ln Y / L with

(15.5)

b

Unfortunately, it is not possible to be content with this assumption that the pace of innovation was steady along the three stages of the evolution of the US economy. In our analysis of the historical profile of the profit rate, we already mentioned that the dramatic restoration in the intermediate stage must be linked to an accelerated pace of technical progress. It is, therefore, possible to say that the relationships between labor cost and technology are not "historically stable."6 In the formalism above (equations 15.3 and 15.4), the absence of historical stability is reflected in the fact that some of the parameters a, b, c, and d may depend on time. Empirical analysis reveals that the relationship between w and Y / L was quite stable (i.e., c and d in equation 15.4 remained constant over a period of more than a century). Concerning equation 15.3, only a varied over time, from a value, ai, in the first stage to another value, a3, in the third stage. These findings suggest the following interpretation: 1. The direct dependency of the capital-labor ratio on

labor cost was maintained during the three stagesto the effect that the same percentage of growth of the labor cost always pushes firms into the same percentage of growth of the capital-labor ratio (stability of parameter b). 2. The unusual acceleration of technical progress was, in fact, superimposed on this relationship during the intermediate stage. We represent the transition of a(t) between ai, its value during the first stage, and a3, its value during the third stage, by a logistic curve as in the representation of

272

Technology and Distribution

the leap forward in chapter 14 (see appendix 14.Al for the notation and the interpretation of the parameters in the logistic). The model can be written as follows:

a(t)

= ai(l -

L(t))

+ a3L(t)

This expression is a simple analytical form that accounts for a continuous movement from one value to another, compatible with a sudden, as well as a progressive transition. A sudden transition would lead to the distinction of two periods interrupted by a break. A progressive transition corresponds to the existence of three stages, with endogenous dating and determination of the duration of the intermediate stage. With the notation l = a3 - ai, the relationship between K / L and w can now be written:

lnK/L = ai

+ lL(t) + blnw

(15.6)

The estimation of this equation yields very significant results, and the values found for the parameters of the logistic show that the transformation culminates during the Great Depression, and that half of the effect was concentrated between 1927 and 1941.7 As could be expected, the parameters obtained for the logistic are very similar to those corresponding to the trend line of the profit rate in figure 14.3. Note that the relationships implied in the description of technological change in relation to labor cost have globally been very stable. Only one parameter of four appears to have varied historically. This variation requires "extraordinary" circumstances, which overstep the limits of the simple linear model in equations 15.3 and 15.4. This movement was initiated at the turn of the century when the low levels of the profit rate threatened accumulation and stability, and social tensions were exacerbated by the increased resistance of enterprises to the rise of labor cost (see chapter 19).

Historical Tendencies

273

There is a strong similarity between the economic junctures at the end of the 19th century and at the end of the 20th century. In both cases the profit rate is low, and the necessity of an important transformation is urgently called for. Consequently, the issue is raised of a new acceleration of technical progress in recent trends. There is no doubt, in this respect, that the regularities described above may have been subject to new disturbances since the late 1970s. However, these movements are too recent to permit a treatment similar to that given to the wave of technical progress described with the logistic curve for the intermediary period. The difficulty of the appraisal of recent trends is compounded by the occurrence of comparatively large fluctuations in prices. For these reasons, we will have to accept passively the first signs of the deficient explanatory power of the model for recent years. 15.6 Empirical and analytical results

Adding the definition of the profit rate to the equations introduced in the two previous sections, a model with four variables and four equations is obtained. The estimation of equation 15.4 reveals that the value of the coefficient of ln w is very close to 1. We will, therefore, assume in the rest of this chapter that this coefficient is exactly equal to 1. This assumption considerably simplifies the estimation and analytical treatment of the model. The following model is, thus, adopted: K ln L =

ai

+ lL( t) + b ln w

with L( t) as in equation 14.2 y ln- = c + lnw L p(w) = f + gp(r) + hlnr

(15.7)

(15.8) (15.9)

274

Technology and Distribution

Figure 15.2 Labor productivity: series (•) and models (o and.) Y/L

20.0~;

..

15.0 ! I

10.0

f; Q•• •..

.f

5.0

/

3.0

/

rf

2.0-----.---....-----..-------..---.-----, 1860 1880 1900 1920 1940 1960 1980 Yea.r

Figure 15.3

Capital-labor ratio: series (•) and models

(o and.) K/L 30.0 I 20.0

.• T

15.0 • 10.0

5.0

3.0 2.0

1.5-+-----..-------------.---.----, 1860 1880 1900 1920 1940 1960 1980 Yea.r

Historical Tendencies Figure 15.4

275

Labor cost: series (•) and models (o and.)

w

.• 10.0 . .

15.0

I

/ ,..

I

r

'-/ ~.

5.0

/

~

3.0

...... ~·

2.0 1.5 1860

.J

1880

Figure 15.5

1900

1920

1940

1960

1980

Year

The profit rate: series (•) and models

(o and.)

Technology and Distribution

276

r

_

(~ -w); ~

In order to improve the estimation of the model, it is useful to incorporate into the regressions two variables characteristic of the shorter-term fluctuations of the series. To account for the effects of business fluctuations, we will use the proxy capacity utilization rate u (figure 14.4). In a similar manner, for the effect of long-term fluctuations of labor cost w, we use variable v = Zn.@ introduced in appendix 15.Al and displayed in figure 15.6 (o). (Short. and long terms are used in the precise sense that we give to these notions, cf. chapter 9.) The estimation of the model is quite satisfactory (see appendix 15.A3). The quality of the fit is illustrated in figures 15.2 to 15.5. Each of these figures displays three lines: ( 1) The original series ( •), ( 2) The reconstruction of the trends and historical fluctuations (.), and (3) The full-fledged reconstruction of the series using the variables which account for the effects of short- or long-term fluctuations (business fluctuations and longterm deviations of labor cost from its trend) ( o). It is striking, in particular, that the four historical fluctuations are so precisely reproduced once the features of technological change in the intermediate stage have been acknowledged. It is also possible to study this model analytically (cf. appendix 15.A4), and demonstrate the following properties: 1. If one abstracts from the accelerated pace of innovation in the intermediate period, the model accounts for a historical trajectory ala Marx: labor cost, labor productivity, and the capital-labor ratio rise exponentially, in combination with an exponential decline of the profit rate. 2. A larger rate of innovation, such as that observed in the intermediate period, temporarily "relaxes" the antagonism between the movement of labor cost and

Historical Tendencies

277

that of the profit rate, and allows the simultaneous increase of the two variables. 3. The impact oflow levels of profitability on the growth rate oflabor cost provokes a slowdown in the evolution of all the variables. The mechanical extension over time of this phenomenon would lead the economy to a standstill-some kind of "stationary state" a la Mill.

15. 7 General interpretation These three results summarize our overall interpretation of the historical trends which prevailed in the US economy since the Civil War. A historical pattern of evolution a la Marx was interrupted during the first half of the 20th century by an acceleration of technical progress, creating a profile in three stages in the movement of most variables. The "recent" slowdownwhich is not limited to labor productivity, but affects all variables-is a new manifestation of the same basic relationships among the variables as in the late 19th century (and not the expression of new properties of capitalism). Although the notion of direction of causality is always ambiguous in a network of interactions, note that, in the analysis of recent trends, the cart has often been placed before the horse. It is important to grasp the specifics of this analysis: the low levels of profitability actually "explain" the slowdown, and not the other way around as is common in the literature.8 More generally, in an analysis such as that developed in this chapter, no specific variable must of necessity dominate over the others. The truly relevant notion is that of the historical dynamics of an intricate web of interdependance among the variables. The profile of historical tendencies is determined by these relationships and the existence of still "autonomous" components, in the sense that they are not directly explained by the variables in the model and require the explicit

Technology and Distribution

278

consideration of time. In this respect, our analysis still encompasses two crucial autonomous movements: the historical trend of the labor cost ( e + ft in equation 15.1) and the acceleration of technical progress (L(t) in equation 15. 7).

NOTES With the exception of the two papers, Boyer R., Juillard M. (1992) and Gordon D. (1991) (presented at the URPE Program at ASSA, New Orleans 1992), few models in the recent heterodox literature have addressed the issue of the historical dynamics of technology and distribution. 2. In the definition of the real wage, the nominal wage would be deflated by the consumer price index to account for the purchasing power of labor. With labor cost, the perspective is not that of the worker, but that of the firm, and the wage must be deflated by the price of the product. The two deflators have similar historical profiles. 3. See Kaldor N., Mirrlees J .A. (1961) and Verdoorn P.J. (1959). 4. It is actually compatible with a vision in which the movements of distribution are important to the explanation of business fluctuations because they affect the levels of demand in the economy. (cf. section 13.3). 5. Stability here has a meaning thoroughly different from that given to the term in the analysis of the stability of a dynamic system. 6. Within econometric literature, what we denote as historical relationships are called long-term relationships. The existence of such relationships can be approached in term of cointegration (Engle R.F., Granger C.W.J. 1987). The application of these methods to the description of technological change leads to the same conclusions as above (see Dumenil G., Levy D. 1991(f)). 7. The estimation of this equation yields t = 34.0 (t = 46.7), b. 6.2 (t 5.6), a 1 0.238 (t 4.6), and l -0.940 (t 7.1). The R 2 statistic is greatly improved (0.981 instead of

1.

=

=

=

=

=

=

Historical Tendencies

8.

279

0.948 for equation 15.3). The value obtained for ..:l seems a bit low. A more satisfactory estimate is found in the estimation of the entire model (cf. appendix 15.A3). There is some relevance in the judgement that the falling profit rate follows from the "productivity slowdown," if the expression refers to the vanishing of the exceptional features of the intermediate period.

280

Technology and Distribution

APPENDICES 15.Al Relationships between w and r: short-term, long-term, and very long term (historical fluctuation) In addition to the positive correlation between the two historical fluctuations considered in section 15.4, two slwrter-term relationships are also evident: 1. Due to the effect of business fluctuations, w and r are positively correlated in the short term. This relationship actually reflects the short-term fluctuations of both variables. First, the profit rate mirrors the fluctuations of the capacit.v utilization rate. This is the Keynesian component of these phenomena. Second, the real wage is also procyclical and influenced positively by large capacity utilisation rates (and conversely during depressed junctures). 2. Once this short-term effect has been taken out, a negative correlation becomes apparent since labor cost, as a cost, impacts negatively on the profit rate. This second relationship is characteristic of the long term, and could be christened "Ricardian." Note that it belongs to what has been denoted as long-term dimension in chapter 9. Interestingly, it is possible to identify these various relationships empirically. Each variable can be broken down into four components: short term, long-term, historical fluctuation, and a linear trend (see appendix 15.A2). The results of this investigation can be subsumed as follows: 1. In the short term, the two variables, r and w, move procyclically, strongly for r, and to a lesser extent for w, but still significantly. 2. The long-term "Ricardian" components, lnFt and ln~it, for the two variables, are displayed in figure 15.6. A negative correlation is now evident, with a correlation coefficient of -68 percent. Large labor costs are reflected negatively in the profit rate, since technology is only slowly affected by the variation of labor cost. 3. The historical fluctuations of the variables around the linear historical trends, denoted ln ¥t and ln 'iiit, have been already discussed in section 15.4 and displayed in figure 15.1.

Historical Tendencies

281

Figure 15.6 Long-term fluctuations of the profit rate (•) and labor cost (•) lnw, lnr 0.08

0.06

6"

v

. .J. : ~~o

J{: ,fi~.1:- ~;.

0·04

0

o·

.---

_ , ..-.

tn . o":

~ \a-:.' .• ·•

• 1.~ .;

d·

.,

~'b

!" .

:; ..:: :. :•\:~ ·. '-'t. ::: :i. ; :~ ~ :.· ; :db~~;: iP. o. • is ifR. .• oo ,,,• ·;·~-····-..:···--···~··~i~~~~-!·i~~.iS-···~..---~..t···~--··-'·-~~~~-~-q;--·

0. 02 0.00

0 ;.. • • •

~

.,..

•••••

.... !I' ........

•

o~

,

••••

- : "~~.

..

..

'r\~ fi~ r~.. ~J~1·j t\i~~t~r·~

-0.02 -0.04 -0.06

~~ : :; ...:c:P: ~

~~ ..

-0.08

i

•silo

.;•)·~

. . +.: ,; :.; 0

:.;

-0.10 ,; -0.12-+-~~~·~~~~~~~~~~~-.-~~..........~~~ 1860 1880 1900 1920 1940 1960 1980 Yeax The vertical scale corresponds to ln$ = v. ln~has been multiplied by 0.1757.

15.A2 Decomposition into four components The Whittaker filter (cf. appendix 11.A3) allows for the decomposition of a variable Zt into two components, its trend, Z"t, and its fiuctuation around this trend, Zt. We modify this filter in order to decompose Zt into four components: (1) A linear historical trend, (2) A historical fiuctuation, (3) Business fiuctuations, and (4) A residual. First, Zt is decomposed into a linear trend, a + {3t ( corresponding to an exponential growth of the variable) and, ~t. its historical fiuctuation around this trend. Second, Zt is broken down into a term refiecting business fluctuations, assumed proportional to the (proxy) capacity utilization rate U.t, and a residual it. The program to be solved is defined by: min

(i.),(i°, ),a,,6 •Y

H

s.t.

Zt

= (a+ {3t + ~t)

1989

with

H =

L

t:1869

t:1871

+ b'u.t +it)

282

Technology and Distribution

The focus of this study is on historical trends and historical fluctuations. Therefore, we chose a comparatively large value for >.: >. = 5000. Since the capacity utilization rate accounts for the short-term component, the long-term component is part of the residual. This method is applied to the labor cost and profit rate in section 15.4, and reveals the existence ofa positive correlation between the two historical fluctuations and a negative correlation between the two long-term components. The method also confirms that the dependency on u of w and r is positive in both cases (;,,, = 0.21 and..,.,. = 1.54), creating a positive short-term correlation. The two variables are positively correlated with a correlation coefficient of 89 percent.

15.A3 Estimation of the model The relationships described by the equations of the model (equations 15.7 to 15.9) concer11 the historical trends and fluctuations, and it is necessary to use appropriate econometric methods. The most straightforward procedure here is to use the logarithms of the variables. It is not possible, in particular, to use the growth rates of the variables, as is common in many econometric works which deal with business fluctuations. For the model in which the effects of the levels of the profit rate are not considered (h = 0 in equation 15.9), there would be little difficulty in expressing the logarithms of the endogenous variables as functions of the logarithms of the exogenous variables in each equation. Unfortunately, this is not possible in the general case. Consequently, the estimate of the general model will be performed using a form of the model in which the logarithm of each variable is explicitly expressed as a nonlinear function of time (see appendix 15.A4). For darity, the results will, however, be presented in the original display of the model as in equations 15.7 to 15.9. We estimate this nonlinear model with the procedure MODEL (method SUR) of SAS/ETS, and obtain: ln KL = -

+

0.440 -

(t=5.0} 2.67

(t=16.5}

3.12

(t=9.5} ln w -

(1- 1 / (1

0.289 u

(t=4· 7)

+ ezp t - 334 ·6 ))

+ 0.523

(t=2.8}

1 .5

v

(15.10)

Historical Tendencies y ln - =

L p(w)

2.67

(t=16.5}

+ ln w +

0.525

u-

0.128 v

(t=23.6} (t=1.9} = 0.0414 + 0.396 p(r) + 0.0181 lnr (t=22.3} (t=19.5} (t=12.0}

+

0.184 u

(t=9.0)

+

1.10

(t=12.0}

v

283 (15.11)

(15.12)

Student's ts for the two parameters, t = 34.6 and A= 13.5, in the logistic are t = 86.5 and t = 22. 7 respectively. A last parameter '(), as in equation 15.13, which is linked to the values ofr0 and wo, is also determined: ;p 4.63 (t 9.0). As might be expected, the most significant coefficients of u is obtained for labor productivity (equation 15.11), and that ofv is found for labor cost (equation 15.12). However, the other coefficients are also significant (or nearly for v in equation 15.11). Consider first the impact of the capacity utilization rate. The signs of the coefficients show that:

=

=

1. Output is more cyclical than labor (equation 15.11).

2. Employment is more cyclical than capital (equation 15.10). 3. The growth rate of labor cost is procyclical, i.e., the growth rate of the nominal wage is more cyclical than that of the NNP deflator, the rate of inflation (equation 15.12). Consider now the impact of the long-term fluctuations of labor cost. The signs observed for the coefficients of v suggest that: 1. There is a positive capital deepening effect (equation 15.10).

2. The long-term fluctuations of labor cost impact negatively on labor productivity, possibly via their depressing effect on the profit rate and, consequently, on investment and demand (equation 15.11). Note that the sign found contradicts the view that the rising wage stimulates consumption and, thus, impacts positively on output, or that the rise of labor cost diminishes employment and, thus, increases labor productivity.

15.A4 Analytical treatment of the model Eliminating three variables in equations 15. 7 to 15.9, and with ln A(t) = -lL(t), one obtains a differential equation for the fourth

284

Technology and Distribution

variable, for example, r:

p(.,.) "Y

.,. + ,13 ln = .,. = -yp(A)

= 1/(1+g(b-1)),

with .13 = h(b- 1)1',

and

lnr =

-! /h

The resolution of this equation yields an explicit expression for r as a function of time: ln.,. = ln r

+ e-/jt

(

'P - "Y

1°"

e/Jr p(A)dT)

(15.13)

The remaining variables can, then, be expressed as functions of time. For w, one obtains: ln w = - 1b (E -1

+ ln A(t) -

lnr) with E = ln (e:z:p(c) - 1) - a 1

ln(K/L) and ln(Y/L) can be derived from equations 15.7 and 15.8.

16. Accumulation and Growth The list of economic effects emanating from the profit rate has been continuously extended along the parts and chapters of this book-with respect to competition and the formation of a long-term equilibrium in parts II and III, in relation t.o the stability of the macroeconomy in part IV and, finally, concerning technological change and wage determination in the previous chapter. The present chapter deals with accumulation, and adds one further item to the list.. The basis of the relationship between profitability and accumulation is that capital accumulation is financed out of past profit. Thus, a low profit rate should result in a reduction in the pace of accumulation, and vice versa. This view echoes the classical conception of accumulation: the growth of the economy is determined historically by its ability to save and invest. This chapter first describes the pace of accumulation and its relation to profitability. Then the model in chapter 15 is developed, adding a new equation for accumulation. A brief comparison between the classical and Keynesian conceptions of accumulation and investment is presented in an appendix. 16.1 The pace of accumulation The stock of fixed capital considered here is the sum of structures and equipment, net of depreciation, for the private economy, as in chapters 14and15. Accumulation in one year is defined as the variation of the capital stock, now measured in constant dollars, i.e., net investment. 285

Technology and Distribution

286

Tl1e stock of capital: series (•) and model

Figure 16.1

(o ), billon dollars (1982) K

5000 3000 2000 1000 500 300 200 100 50+-~~-r--~----.~~--.-~~-.,-~~-r-~~...--~---,

1860

1880

Figure 16.2

1900

1920

1940

1960

1980

Year

The rate of accumulation and its trend

0.35 0.30

..

. .

0.25 0.20 0.15 0.10 0.05

0.00-+-~~~~~~~~~~-=-··~=-·~~~~~~~--. 1860

1880

1900

1920

1940

1960

1980

Year

The negative rates observed during the Great Depression have been omitted.

Accumulation and Growth

287

Figure 16.1 ( •) describes the evolution of the capital stock since 1869. Its pattern of evolution is reminiscent of the profit rate and other variables in the previous chapters. The intermediate period in which the profit rate is low coincided with a slackening of accumulation. The growth of the capital stock was successively fast, slow, and fast: 4.65 percent for 1869-1912, 0.70 percent for 1912-1951, and 3.52 percent for 1951-1989. (A slowdown can be observed in the 1980s.) A very strict translation of the relationship between accumulation and profitability is to assume that a constant fraction of profit, the rate of accumulation a, is accumulated, i.e., Kt - Kt-1 = allt-1 · W'ith this assumption, the profit rat.e determines the rate of growth of the stock of capital, (Kt - Kt-1)/Kt-l = allt-if Kt-1 art-1, i.e., the well-known relation:l

p(K) = ar

(16.1)

The assumption of a constant rate of accumulation may be meaningful in what we call the long term, but it is not clear that it makes sense historically. Note parenthetically that this is probably the reason why Marx associated the tendency for the profit rate to fall with an increasing rate of accumulation: A fall in the profit rate, and accelerated accumulation, are simply different expressions of the same process, in so far as both express the development of productivity. (Marx K. 1894, Ch.15, p. 349)

Figure 16.2 plots the value of the rate of accumulation a for the period 1869-1989.2 Two plateaux are evident in this profile: from 1869 to World War I a first large value is observed, whereas a new rate prevails after World War I. In spite of the large fluctuations in the profit rate, the rate of accumulation displays a horizontal trend since World War I. Figure 16.2 also presents a trend line which illustrates

288

Technology and Distribution

this pattern of evolution.3 It accounts for a dramatic shift, of 13.9 percent, in the rate of accumulation from 24.8 percent to 10.9 percent, centered around 1914.4 Two remarks must be made concerning this shift in comparison to that observed for the other variables. First, the shift does not. occur in the same years as for the variables accounting for technology and distribution. Second, the transition seems faster. Although we cannot provide a satisfactory interpretation for the sudden fall around World War I, it is important to keep in mind that the US economy underwent a number of transformations of major importance during the period considered: 1. World War I also coincided with important transformations in finance, property relations, and firm management. For example, in the early years, the relative weight of self-employed persons in the total economy was considerable, and was then reduced progressively. An hypothesis is that this category of entrepreneurs ploughed back a large fraction of their income into their own business. 2. A dramatic shift in the general level of prices occurred, and a new actor, government, became increasingly invoived in the division of profit. in relation to the rise of taxation in the following decades. One should also remember that the measure of accumulation considered here concerns fixed capital, i.e., only one component of total capital. The sudden peak of the rate of accumulation in the mid-1880s is puzzling. Such variations may be related to the movements· of foreign investment into the US. However, it is also true that this observation sheds doubts on the capital stock series in these years.5 The above remarks should not divert our attention from the major finding which follows from this investigation: after an important shift downward in the value of the rate of accumulation, its historical trend remained constant for a considerable period of time-nearly 80

Accumulation and Grovrth

289

years since the decline. 16.2 A model of accumulation In chapter 15 a model was presented which accounts for the evolution of technology and distribution. The variables considered were labor productivity, the capitallabor ratio, the profit rate, a11d labor cost. In the present section, we will show that the addition of the above very simple accumulation model in equation 16.1 -with a dummy variable accounting for the break i11 the rate of accumulation detected around World War I -is sufficient to reproduce the historical profiles of the main variables quite satisfactorily: the capital stock, the product, and the number of hours worked. As in chapter 15 we include in the model the two variables, u and v, which measure shorter-term fluctuations of the general level of activity and labor cost. The dummy variable is denoted D 1914 • The model for a is the following: a = ao

+ a1 D 1914 + auu + avv

(16.2)

Its estimation is described in appendix 16.A2. Note that the shift in the rate of accumulation, i.e., the coefficient of the dummy variable, is estimated at 8.6 percent instead of 13.9 percent above. This measure, though more realistic, is still large. The reconstruction of the series of capital stocks is displayed in figure 16.1 ( o ). The quality of the fit is quite satisfactory. From the above reconstruction of the capital stock and those of the capital-labor ratio and productivity of labor in chapter 15, one can derive the number of hours worked and the net product: K

L

= (K/L)

and

y

= K(Y/L) (K/L)

(16.3)

290

Technology and Distribution

Figure 16.3

The number of hours worked: series (•) and model (o ), billion hours

L

200 150 :

. T

100

50

30 204-~--.-~~....-~--.-~~....-~--.~~....-~--.

1860

1880

Figure 16.4

1900

1920

1940

1960

1980

Year

The Net National Product: series (•) and model (o ), billion dollars (1982)

y 5000 3000 2000 1500 1000 500 300 200 150 100 504-~--.-~~....-~--.-~~....-~--.~~....-~---.

1860

1880

1900

1920

1940

1960

1980

Year

Accumulation and Growth

291

The results of these reconstructions are presented in figures 16.3 and 16.4. The fit for the number of hours worked after World War II is less satisfactory than for the two other variables. This problem is similar to the difficulty we met in the reconstruction of the capital-labor ratio in chapter 15 (cf. figure 15.3). 16.3 General interpretation

Globally, this analysis suggests the following interpretation: 1. The capital stock (figure 16.1). The dramatic slowdown in the growth of the capital stock after World War I results from the combination of an autonomous shift downward in the rate of accumulation (the fraction of profit devoted to accumulation) and low profit rates. The restoration of the profit rate after World War II permitted accumulation to resume, albeit the reduced rate of accumulation was maintained. The slowdown in the 1980s can be attributed to low profit rates. 2. The number of hours worked (figure 16.3). In the interpretation of the profile of this variable, it is useful to write equation 16.3 in terms of growth rates of the variables: p( L) = p( K) - p( K / L ). The slowdown of accumulation during the intermediate period coincides with that in the growth of the capital-labor ratio. This latter movement is not sufficient to offset the slow growth in the capital stock, and the number of hours worked increases very slowly. After World War II, the pace of accumulation is increased, but the capital-labor ratio also rises quickly, and the number of hours worked grows slowly in comparison to the trend prevailing before World War I. 3. The Net National Product (figure 16.4). The historical trend of the product is surprisingly linear. This movement results from the coincidence of the reduction of the growth in the capital stock and the rise of

292

Technology and Distribution

the productivity of capital in the intermediate period. The recent slowdown in the growth of NNP mirrors the reduced growth of the stock of capital and its declining productivity (since p(Y) = p(K) - p(Y/ K)).

NOTES 1.

2. 3. 4.

5.

It is important to distinguish between the rate of accumu-

lation (the share of profit devoted to accumulation) and the growth rate of the capital stock. Figure 16.2 displays the value of (Kt - Kt-d/ IIt-1 in each year. This line corresponds to a logistic trend (following the procedure used in previous chapters). As shown in the next section, the methodology used here overestimates the importance of this shift. This variation is amplified by the surge in the 1890s and the fall into the 1930s. This is precisely the period where the two sources Goldsmith R.W. (1952) and Kendrick J .W. (1961) differ. Such differences are not too disturbing as long as the capital stock is considered as in figure 16.1-where the observations for the 1890s are slightly above the trend-or for the computation of the profit rate. But in a calculation where the growth rate of the capital stock is implied, these deviations are manifested as major fluctuations.

Accumulation and Growth

293

APPENDICES 16.Al Classical and Keynesian conceptions of the formation of capital: accumulation vs inducement The accumulation of capital is an important element in the broad system of interactions which defines the contours of historical tendencies. This point of view is quite characteristic of the classical perspective. This does not mean, however, that capital accumulation is not part of other trains of thought. Below, we will briefly compare the classical analysis of accumulation to the Keynesian analysis of investment. Needless to say we can only scratch the surface of this problem. In the Keynesian tradition, investment is also a function of the profit rate, but not in the sense that profit provides a financial basis for investment. A "sufficient" expected profit rate (marginal efficiency of capital), it is argued, must exist to induce capitalists to invest their capital or, in another formulation, a higher expected profit rate will trigger a higher level of investment. In the classical analysis of the formation of prices of production, capital is guided, in its migration from one industry to another, by profitability differentials. In this sense, investment is clearly dependent on expected profitabilit.v. However, the issue now is that of the consequences of the level of the average profit rate in the economy on the level of total investment. The fact that the marginal efficiency of capital is an expected profit rate has important consequences for the volatility of investment. It is not clear from Keynes' analysis, whether the expected profit rate is related to the actual rate. In Chapter 22 of the General Theory, Ke.vnes asserts that investors on financial markets are often "ignorant" of the actual yield on capital assets! Keynes blamed business fluctuations on "psychology" ("animal spirits"). It is difficult to empirically distinguish between inducement and accumulation. Inducement suggests that profit rates in the future are the crucial variables, while accumulation should focus on past profit. With this simple criterion, empirics favor the thesis of accumulation. The correlation coefficients between various lags of the profit rate and the rate of accumulation are displayed in table 16.1. The best results are obtained with a positive lag for the profit rate (i.e., 1· is leading over p(K)).

Technology and Distribution

294

Table 16.1 - corr(rt-TiP(Kt)) -4

-2

0

2

4

6

8

-0.02

0.21

0.42

0.45

0.48

0.50

0.42

T

16.A2 Estimation of equation 16.2 (rate of accumulation) Since the growth rate of the capital stock is small, it can be estimated as ln Kt - ln Kt-i. and equatio11 16.1, with the model for a: as in equation 16.2, can be written: ln Kt - ln Kt-1 =

(a:o

+ a:1D~ 914 + O:uUt + a:,,vt)rt-1

(The dummy variable Df 914 is equal to 1 prior to 1914 and zero after.) We sum this expression for t, t - 1, · · ·, 1870, and obtain: ln Kt = ln K 1869 + a:oRt

+ 0:1 R~ 914 + a:u Ut + a:,, vt

(16.4)

in which: t

t

Rt=

L

r.--1

.-=1870

L

rr-1D~914 =

r=1870

t

Ut =

min(t,1913)

L

~914 =

r=1870

t

L

L

Vi=

r.--1Ut

r=1870

rr-1Vt

r=1870

The estimation of equation 16.4 yields: ln Kt =

10.9

(t=455.}

+

0.894

+

(t=3.6}

0.0881 Rt

(t=70.5}

+

0.0864 ~ 914

(t=21.9}

+

0.665 Ut

(t=9.9}

Vi

In addition to the results set forth in section 16.2, one can notice that the coefficient a:,, is positive. It reveals that a rise oflabor cost above its trend value stimulates accumulation (probably because of the inducement toward mechanization), and that this movement corrects for a fraction of the negative effect of the rise of labor cost on the profit rate.

1 7. Profitability Trends The definition of the profit rate used in the previous chapters combines a very broad definition of profit, the fraction of the national product which does not go to labor, and a narrow definition of capital, reduced to fixed capital. This definition is well adapted to the analysis of technological change and primary distribution, but it abstracts from other important aspects of the economy. As contended in the second chapter of this study, other definitions of the profit rate must also be considered. The analysis in this chapter is devoted to several such definitions which refer to other components of capital and other units of analysis. This investigation illustrates the view that the network of relationships described in the two previous chapters must be considered as part of an even more general system of interrelations. It emphasizes, in particular, the role played by economic agents, other than enterprises or employees, such as the state, and relates firm profitability to a number of institutional transformations.

17.1 The impact of taxation The historical evolution of firm taxation is well known, and the analysis of its evolution will remain beyond the limits of the present investigation. It is clear that taxes must be subtracted from profit, whenever the analysis focuses on the consequences of profitability on firm behavior (such as investment or management in general), instead of its origins. This 295

Technology and Distribution

296

Figure 17.1

,.

The impact ofta.xation: pre-(•) and after(o) corporate profitability (1929-1989)

tax

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10

:

..

.

.~. ·"'·..•. ,",

• fl fl

"•..

.. ..·.

~

·~·

....

·

·-.

...

.

··."· .. ... .....

.....··~ ·~...

~

•

0.05 0.00 -0.05-+---.-----.----.----..------.----.-----. 1920 1930 1940 1950 1960 1970 1980 Year

deduction is important, since the profiles of pre- and after-tax profitability differ significantly. In order to investigate this phenomenon, the unit of analysis is restricted to the corporate sector (now 71 percent of income in domestic private business), for which data series on both indirect business taxes and corporate profit taxes are available. Figure 17.1 displays the profit rate since 1929, for the corporate sector, gross of taxes ( •) as in figure 15.5 and net of all taxes ( o ). It appears, thus, strikingly that the leap forward in profitability documented in chapter 14 was completely absorbed by the state through taxation. In the first measure ( • ), the profit rate is equal to 15.8 percent in 1929 and soars to an average of 27.1 percent for the period 1946-1955. In the second measure, the leap is totally offset, and the series actually displays a dedine.1

Taxes from enterprises represent a considerable fraction of public receipts. Excluding social insurance con-

Profitability Trends

297

tributions, these taxes amounted to about 80 percent of public receipts in 1929 and during the depression. After World War II, this percentage diminished because of the rise of personal income taxes, but they still represented about 60 percent of total receipts. The above percentage was reduced to about 45 percent in the 1980s. An examination of these series strongly supports the view that, beyond the obvious accounting impact of taxation on profit, there is a feedback effect of the profit rate on taxation. The surge of profitability through the depression and the war allowed the rise of taxation and the transfer of profit from firms to the state. Symmetrically, the decline of the profit rate since the war resulted in the progressive alleviation. of the burden placed on enterprises, in spite of the increasing difficulty to balance the budget of the state. We want to emphasize the implications of this analysis in two important respects: 1. This reciprocal link between profitability and taxation is similar to that introduced in chapter 15 between the profit rate and labor cost. First, there is an accounting aspect implied in both cases: a rising labor cost and a larger tax rate encroach on the profit rate. Second, two similar feedbacks are involved: large profit rates allow simultaneously a faster growth of labor cost and a larger transfer of profit to the state. These observations provide serious grounds supporting the hypothesis of a kind of very-long-term "control" of the profit rate. 2. The level of the profit rate is an important determinant of stability. The transfer of profit to the state is detrimental to this stability since the profit rate accruing to enterprises is diminished. However, large state expenses are stabilizing, because of their stickiness, and it is difficult to a priori determine the outcome of such conflicting influences.

298

Technology and Distribution

1 7 .2 Inventories and money In the definitions of the profit rates used so far, the measure of capital was limited to fixed capital. As manifested in firm balance sheets, two other major components of total capital should also be considered, inventories and financial assets. Inventories of goods in process and finished goods are maintained in those sectors of the economy in which goods are produced, such as Agriculture, Manufacturing, and Mining. Obviously, large inventories of finished goods are also held in the trade industry. Inventories of "raw materials" are required in every industry. For several reasons, the consideration of the financial and monetary components of capital is more difficult than that of real components. It would not be correct to include all financial assets in the measure of total capital, since important fractions of these assets mirror the existence of reciprocal relationships among firms, such as trade credits. We will limit the investigation here to currency and demand deposits, as a narrow definition of the balances of liquid purchasing power held by firms for transaction purposes. Figure 17 .2 compares the profile of the profit rate as in figure 14.3, with a measure including inventories and currency and demand deposits.2 One can notice in this figure that a significant leap is still observed during the depression and World War II in the second measure ( o ), but that no clear downward trend is evident after World War II. The decline since 1946 of the first measure, with fixed capital only, is almost totally offset in the second measure, when inventories and money are considered. It is therefore clear that the inclusion of other components, in addition to fixed capital, provides supplemental information in the assessment of the historical profile of the profit rate. It is heipful in the interpretation of the trends of the two profit rates in figure 17 .2 to consider the three

Profitability Trends Figure 17.2

299

The profit rate: profit over fixed capital (• ), and fixed capital, plus inventories and money (o)

r

.

0.50

•:

0.40

••i :

•.

\ n}i~· · ·. .