Capital Theory Controversies Research Articles

Investment function in Marshall, Fisher and Keynes: a critique of the neoclassical theory of investment in light of the capital theory controversy

An overwhelming majority of the economics profession is taught that there is an inverse relationship between interest rate and investment expenditures. In the light of the controversies in the theory of capital, we analyse in this article the way in which Marshall, Fisher and Keynes have constructed this inverse relationship. All three were aware of the problems associated with this construction and tried—albeit unsuccessfully—different ways to get around them. This implies that within the neoclassical analysis there does not exist a theoretically consistent conceptualisation of an investment demand function inversely responsive to the rate of interest.

On the Relationship between the Money Rate of Interest and Aggregate Investment Spending

Careful observers had already pointed out before the capital theory controversies that an investment demand schedule inversely responsive to the rate of interest is theoretically untenable. This implies that the weak empirical evidence showing the negative relation between aggregate investment spending and the rate of interest cannot be explained via the neoclassical investment theory. Assuming a short-run framework and concentrating on the “Sources and Uses of Funds Account,” it is shown here that the inverse relationship between the two variables derives, not from the investment demand function, but from the ability to finance investment spending. The explanation is valid only in the short run. In the long run, aggregate investment spending may rise, fall, or remain constant in response to a change in the rate of interest. JEL Classification: B51, E11, E22, G31

After the Cambridge Controversies: Reflections Old and New

Abstract Perfect foresight is a consequence of applying the Pontryagin Maximum Principle to the analysis of an intertemporal general equilibrium. For this reason, the capital theory controversy ended in an intellectual impasse. The critique of mainstream theory largely ignored the perfect foresight entailments of intertemporal equilibrium analysis, while its defenders, with notable exceptions, too often failed to acknowledge this implication of the technique of dynamic programming. From this standpoint, the long debate over the existence or non-existence of an aggregate production function is secondary. This leaves open the theoretical question of how to proceed with an analysis of the actual dynamics of capitalist development. The critique of mainstream capital theory remains a ‘prelude’, caught up in an ever deeper analysis of the implications of alternative representations of the technique of production. The first part of this paper deals with the question of how perfect foresight came to infect mainstream theory; the second part turns to a consideration of a weakness in the dual representation of the technique of production in the simplest Sraffian framework. Neither part addresses the bigger questions of how to analyze the process of uneven development under the capitalist rules of the game.

Neutral technical progress and the measure of value: along the Kaldor–Kennedy line

Abstract In this paper, I investigate the question of ‘the effect of progress upon distribution’ based on the analyses of Hicks, Robinson, Harrod, Salter, Kaldor, Samuelson and Kennedy. The paper aims to address a neglected and controversial theoretical argument on neutral technical progress related to the measure of value that preceded and then continued to the period of the Cambridge Capital Theory Controversy. I focus on Kennedy’s writings and his solutions to the complications between the measure of value and technical progress. Important intuitions behind the measure of value are crucial to the formulation of neutral technical progress in both the post-Keynesian and the neoclassical-Keynesian endogenous growth models. The paper concludes with mathematical illustrations of neutral technical progress theories.

Austrian themes and the Cambridge capital theory controversies

While Austrian economists and their models were only indirectly involved in the Cambridge capital theory controversies that came to a dramatic head in 1966, certain ideas argued for by the Cambridge, UK side were prefigured in some work by Austrian economists, especially F.A. Hayek in his 1941, The Pure Theory of Capital, which he wote largely as a result of earlier debates with both Sraffa and Keynes. This paper recounts the roots of the capital theory debates coming out of the nineteenth century, the arguments among Keynes, Sraffa, and Hayek, Hayek’s analysis that undermined traditional Austrian views of capital, the Cambridge controversies themselves, and then how various groups followed up in the aftermath, including neoclassicals, neo-Ricardians and Post Keynesians, and various groups of Austrians, who were themselves slow to recognize the full implications of Hayek’s work and its relation to the Cambridge capital theory controversies. A final point is that among both those following Sraffa and Joan Robinson more as well as those following Hayek more, some have seen the issues leading to broader complexity approaches to capital theory and economic dynamics.

Joan Robinson and MIT

Roger Backhouse remarks in “MIT and the Other Cambridge” (History of Political Economy 46, supplement) that the capital theory controversy came to be seen by most of the economics profession as a waste of time. Joan Robinson's 1953 paper “The Production Function and the Theory of Capital” started the controversy. An abbreviated version, published in the second volume of her Collected Economic Papers, made clear that her critique came in two parts. The “constructive” part drew attention to the phenomena of reverse capital deepening and re-switching of techniques and attracted the interest of theorists at MIT and elsewhere. The “negative” part concerned the problem of getting into equilibrium and was, for Robinson, the essence of the controversy. A close reading of the literature shows not only that Robinson was never credited with an understanding of the Achilles' heel that plagues dynamic general equilibrium models, but also that the problem, though variously recognized, was essentially ignored. The suggestion that the capital theory controversy was a waste of time fails to recognize that Robinson had drawn attention to a fundamental unsolved problem in economic theory.

Capital theory ‘paradoxes’ and paradoxical results: resolved or continued?

Capital theory controversies and ‘paradoxes’ showed that, due to price-feedback effects, the wage–production price–profit rate curves may display shapes inconsistent with the requirements of the neoclassical theory of value and distribution. Subsequent findings on a number of quite diverse actual single-product economies suggested that the impact of those effects is of limited empirical significance. This paper argues that, by focusing on the distributions of the eigenvalues and singular values of the system matrices, we can further study these issues and derive some meaningful theoretical results consistent with the available empirical evidence. Consequently, the real paradox, in the sense of knowledge vacuum and, thus, requiring further research, is the distributions of the characteristic values and not really the ‘paradoxes in capital theory’.

Kaldor’s ‘technical progress function’ and Verdoorn’s law revisited

Kaldor put forward his technical progress function as an alternative to the neoclassical aggregate production function. It is shown that Verdoorn’s law is its empirical counterpart, although allowing for increasing returns to scale. However, both may be derived from an aggregate Cobb-Douglas production function. But aggregation problems and the Cambridge capital theory controversies have shown theoretically that aggregate production functions in all probability do not exist. Moreover, the only reason that estimations of ‘aggregate production functions’ give good results is the existence of an accounting identity. This article reconsiders the technical progress function and Verdoorn’s law, especially in the light of these problems. Nevertheless, it is shown that estimates of the law do, in fact, provide insights into the growth process very similar to those of Kaldor, but viewed from another perspective.

Some Unsettled Issues in a Second Phase of the Cambridge-Cambridge Controversy

The aim of this paper is to clear up some issues in a second phase of the Cambridge-Cambridge capital theory controversies, when the neoclassical argument was chiefly conducted in terms of the Walrasian specification of capital in intertemporal and temporary general equilibrium models. It is held that the response by the neoclassical side in that phase has not been as satisfactory to rebut the implications of reswitching and capital reversing as some neoclassical scholars have argued. The reason for this can be traced in the overlooking of the implications of the redefinition of equilibrium implied in those models.

Comment: Lance Taylor on Thomas Piketty’s World as Seen Through the Eyes of Maynard Keynes and Luigi Pasinetti

:This comment discusses Taylor’s critique of Piketty’s model and his extension to bring in insights from Keynes and Pasinetti. In addition, the comment contains criticisms of the meanings of Piketty’s statistical findings, which are based on accounting measures, of Piketty’s failure to understand the significance of the Cambridge Capital Theory Controversies critique for Piketty’s use of the aggregate production function; and an extension to bring in further insights from Keynes and from Marx in order to understand recent historical episodes in modern capitalism.

The Aggregate Production Function: ‘Not Even Wrong’

The foundations of the aggregate production function were long ago thrown into doubt by problems of aggregation and the Cambridge capital theory controversies. Yet the aggregate production function, whether in the familiar form of the Cobb-Douglas, the CES, or the translog, continues to be widely used in both theoretical and applied analysis. The reason for its continued use rests on the instrumental position that ‘it works’. The aggregate production function sometimes yields good statistical fits with plausible estimates of the coefficients. However, for some time, it has been realised that the existence of an underlying accounting identity can explain the regression results, even if the aggregate production function does not exist. This argument has been widely ignored. This paper, drawing on a rhetorical approach, assesses why this is the case. It shows that the few criticisms that have been made of the critique involve fundamental misunderstandings that represent a failure of the economic method.

A few counter-factual hypotheses on the current economic crisis

The economic and financial problems of the present devastating crisis are terribly practical. Sraffa's little book is highly theoretical. To relate the two we must avoid stopping at Keynes, and include the whole group of economists around him in Cambridge, resuming the discussions that have been pushed into oblivion by the mainstream. The capital theory controversy was not the only one. Here, more relevant is the controversy on growth, income distribution, savings and profits between Samuelson--Modigliani and Kaldor--Pasinetti. As a result, a theorem, associated with Modigliani--Miller, was brought to fame and hailed as 'the core of modern corporate finance'. Its surprisingly wide acceptance is here harshly criticised and indicted of major responsibility for the present crisis. Inevitably, this is argued through counter-factual hypotheses. Yet, even with less sophisticated analytical tools, a framework does exist, much nearer to common sense, implying the needed flexibility and openness of mind for the major restructuring of financial institutions, which today so clearly emerges as the major task to undertake. Copyright , Oxford University Press.

C.E. Ferguson and the Neoclassical Theory of Capital: A Matter of Faith

In 1969 the American neoclassical economist C.E. Ferguson wrote that reliance on neoclassical aggregate production and distribution theory is a ‘matter of faith’ to be sorted out (he says ‘answered’) by econometricians. Ferguson was criticized on both sides of the debate for invoking this religious metaphor. Using the methodological framework of A.J. Cohen & G.C. Harcourt (2005), Introduction: capital theory controversy: scarcity, production, equilibrium, and time, in: A. Cohen, G.C. Harcourt & C. Bliss (Eds) Capital Theory, 3 Vols. Northampton, MA: Edward Elgar, this paper argues that faith plays a recurring role in all capital controversies and especially in modern theories of growth that rely wholesale on the aggregate production function. Ferguson's faith proves to be much more insightful than previously recognized.

›Cantabrigian Economics‹ and the aggregate production function

In Cambridge, UK, in the late 1960s and early 1970s, there were some of the most distinguished post-war non-neoclassical economists, which included Nicholas Kaldor, Joan Robinson and Piero Sraffa. The Cambridge capital theory controversies seemed to have been decisively settled in Cambridge, UK's favour, yet no alternative paradigm emerged to challenge the prevailing neoclassical orthodoxy. This paper briefly looks at the reasons for this, including why the Cambridge capital theory debate, despite its important ramifications, is now largely forgotten. The paper concludes by looking at a further problem that vitiates the aggregate production function, resulting from the use of constant-price value data in econometric estimation. This criticism has also been widely ignored.

What is wrong with aggregate production functions. On Temple’s ‘aggregate production functions and growth economics’

In an article in the 2006 volume of this journal, Jonathan Temple presented a defence of the use of the aggregate production function in growth theory in the light of various criticisms that have been levelled at it. These criticisms include the Cambridge Capital Theory Controversies, various aggregation problems, and the problems posed by the use of value data and the underlying accounting identity. We show that Temple has underestimated the seriousness of these criticisms, especially the last one, which vitiates the concept of the aggregate production function. Because of the identity, estimates of putative aggregate production functions, such as the aggregate elasticity of substitution, cannot be interpreted as reflecting the underlying technology, and hence the use of the aggregate production function is extremely problematical.

Whatever Happened to the Cambridge Capital Theory Controversies? <i> (With comments by L. Pasinetti, F. Fisher, J. Felipe and J. McCombie, R. Greenfield and reply by the authors)</i>

The article written by the well-known theorists and historians of economic thought contains a detailed overview of the Cambridge capital controversy, which had raged from the mid-1950-s through the mid-1970-s. The authors track the origins of the controversy and cover arguments of both sides in chronological order. From their point of view, the discussion hasnt been resolved, and its main underlying aspects were ideological beliefs and fundamental methodological controversies on the nature of equilibrium and on the role of time in economic theory. The article is published with comments written by other leading theoreticians.

Why the data tell us nothing about the importance of increasing returns to scale and externalities to capital

It has long been known that, because of aggregation problems and the Cambridge Capital Theory Controversies, the aggregate production function cannot theoretically exist. Nevertheless, the concept is still widely and uncritically used, presumably because it gives good statistical fits to the data with plausible results. It is shown that this occurs because of the existence of an underlying accounting identity. A suitable mathematical transformation of this identity ensures that it is always possible to specify an "aggregate production function" where the putative output elasticities equal the factor shares, even though the aggregate production does not exist. This is illustrated by reference to a simulation exercise by Felipe and McCombie (2006) and a study by Oulton and O'Mahony (1994). The latter reject the hypothesis that capital is "special", in that their regression estimates demonstrate that the "output elasticity" of capital does not significantly differ from its factor share. However, it is shown in this paper why the data could not have given any other result.

The Kaldor/Knight controversy: Is capital a distinct and quantifiable factor of production?

Controversy focuses on three questions: Is capital a distinct factor of production? Is capital quantifiable in a theoretically consistent manner? Are process stories necessary around convergence to, or changes in, equilibrium interest rates? To all, Kaldor answers ‘yes’ to Knight's ‘no’. The controversy is historically important in: 1) shifting issues in recurring twentieth century capital theory controversies from periods of production to production functions, from roundaboutness to diminishing returns; 2) revealing Knight's position on increasing knowledge offsetting diminishing returns over time as an unacknowledged ‘precursor’ of new growth theory; 3) marking the turning point for Kaldor's attachment to Austrian theory.

Capital theory and the origins of the elasticity of substitution (1932–35)

Elasticity of substitution was introduced into economics during the early 1930s. It was discovered independendy by Hicks in The Theory of Wages and by Joan Robinson in The Economics of Imperfect Competition, and then was the centre of a polemic involving Kahn and Sraffa, among others. The debate focused on imperfect competition and capital-theoretical issues. Some elem ents of the 1950s and 1960s capital theory controversy, such as the idea of capital as a Giffen good or the difficulties of measuring capital, were already discussed at this early stage.

Retrospectives Whatever Happened to the Cambridge Capital Theory Controversies?

We argue that the Cambridge capital theory controversies of the 1950s to 1970s were the latest in a series of still-unresolved controversies over three deep issues: explaining and justifying the return to capital; Joan Robinson's complaint that, due to path dependence, equilibrium is not an outcome of an economic process and therefore an inadequate tool for analyzing accumulation and growth; and the role of ideology and vision in fuelling controversy when results of simple models are not robust. We predict these important and relevant issues, latent in endogenous growth and real business cycle theories, will erupt in future controversy.