Category: Capital Theory

On the Capital/Output Ratio

A post on the capital output ratio was perhaps inevitable given my teaching and research engagements with macroeconomics, growth theory, and capital theory. This blog post seeks to critically discuss some of the manifestations of the capital-output ratio (K/Y ratio henceforth) in economics. 

K/Y ratio in Macroeconomics

The K/Y ratio captures a technological characteristic of the economy as a whole. It conveys to us the amount of capital required to produce one unit of output. A reduction in it therefore implies we require less capital to produce one unit of output. 

Since capital refers to the stock of produced means of production, which are of a heterogenous nature, K for the economy as a whole requires aggregation via prices: k1p1+k2p2+…+knpn=K. That is, K refers to, as H. G. Jones puts it (p. 17) in his 1975 book An Introduction to Modern Theories of Growth, “an index of aggregate capital.” Of course, Y too requires aggregation via prices.

Roy Harrod, in the chapter ‘Capital Output Ratio’ in Economic Dynamics (1973) treats K/Y ratio as a “kindred concept of the capital-labour ratio” (p. 46). Subsequently, he outlines the scope of the capital-labour ratio in economic studies. 

“It is to be stressed that the capital-labour ratio is a useful weapon for comparing alternative methods of producing a given object, for comparing methods of producing different objects or for comparing the changes through time of methods of producing a given object. It is on the whole an unserviceable tool in relation to national income as a whole, but it can be employed in a very rough sort of way for comparing different countries” (p. 48, emphasis added). 

Similarly, Harrod writes that “the concept of the capital labour ratio is not very helpful, if applied to the economy as a whole, owing to the difficulty of assessing the value of K, namely capital as a whole” (p. 50). 

Additionally, I think that such an aggregate conceptualization conceals more than it reveals. For instance, it conceals the nature of interdependence of production in an economy. What if K/Y changes because of a change in the nature of structural interdependence? Or, what if it changes because of a change in the volume and composition of aggregate consumption demand? After all, the volume of investment influenced by consumption. As Keynes rightly writes in Chapter 8 of The General Theory, “capital is not a self-subsistent entity existing apart from consumption”. 

K/Y ratio in Growth Theories

The K/Y ratio is used as an argument in Kaldor’s (1957) stylized facts: ‘steady capital-output ratios over long periods’. Here too, what is it saying about the structural nature of production and consumption in the economy? 

While Kaldor is talking about ex-post K/Y ratios, the ex-ante K/Y ratio plays a crucial role in Harrod’s growth equation g=s/v. Here, s refers to the marginal propensity to save and v refers to the desired or normal K/Y ratio. A decrease in v raises g, or more accurately, the ‘warranted rate of growth’. 

In the super abstract setup of the corn model (as in Ricardo) or the single-commodity model (as in Solow), since the input and the output are the same commodity, aggregate K is a homogenous set. This assumption allows us to sidestep the problems associated with the measurement and aggregation of ex-ante K. 

One cannot help but wonder how Solow’s single-commodity growth model (expressed via the aggregate production function) continues to be applied in growth accounting exercises on actual multi-commodity economies. We had noted some of the theoretical and empirical problems with one such exercise on the Indian economy in a short note in Economic & Political Weekly.  

K/Y ratio and Capital Theories

Capital theories are concerned with the conceptualization, measurement, valuation, determination, and aggregation of capital. Owing to the central role capital plays in production, the choice of the capital theory has a significant impact on both microeconomics and macroeconomics. Moreover, since capital accumulation is central to growth theory, the choice of the capital theory has a significant impact on development theories too. Similarly, on international trade theories; on this subject, you can consult the 1979 book Fundamental Issues in Trade Theory edited by Ian Steedman. 

In sum, while mathematization of the growth models gives us a better sense of its grammar, capital theory helps us understand its epistemology. And it is the latter which can better guide the use of K/Y ratio in economic theories, empirics, and policies.  

Some Logical Fallacies in Economics

Economic theory of various kinds are often employed to formulate policies in the real world. Often, certain conclusions of a particular economic theory are utilised in policy making. For instance, some of the insights/conclusions arising from mainstream economics are: fiscal deficits are inefficient and inflationary; a perfectly competitive economy is desirable because it is efficient; increase in money supply causes inflation and increase in investment (domestic and foreign) will create employment. Hence, we are regularly advised to lower fiscal deficits, encourage ‘efficiency’, etc.

Broadly, two kinds of logical fallacies are committed by economists and policy makers. Firstly, there are logical fallacies in the domain of economic theory. Secondly, a logical fallacy is committed when real-world policy decisions are derivatives of conclusions from a particular economic theory. This blog post makes use of Stephen F Barker’s’book‘The Elements of Logic‘(1965) to illustrate some of the logical fallacies in economics.

According to Barker, a ‘fallacy is a logical mistake in reasoning.’ He identifies three broad categories of logical fallacies: (1)’non sequitur, (2)’petition principia‘and (3) inconsistency. Fallacies of’non sequitur‘(Latin: ‘it does not follow’) occur when there is an’insufficient link‘between premises and conclusion. ‘If the premises are related to the conclusion in such an’intimate way‘that the speaker and his hearers could not have less reason to doubt the premises than they have to doubt the conclusion, then the argument is worthless as a proof, even though the link between premises and conclusion may have the most cast-iron rigor,’ logical fallacy of’petition principia‘(Latin: ‘begging the question’) occurs. Lastly, fallacies of inconsistency occur ‘when someone reasons from a set of premises that’necessarily‘could not all be’true.’

Logical fallacies in economic theory

An economic theory like any scientific theory begins from a set of premises. These premises can be based on observation, fact, other theories, (reasonable) assumptions, etc. Obviously, these premises have to be sufficiently’general‘for it to be a ‘theory.’ From these premises, through the process of (deductive) reasoning, we arrive at certain conclusions. Note that unrealistic assumptions do not render an economic theory fallacious. However, their utility in real-world policy making is contingent on how ‘approximate’ the assumptions are to the particular context.

Hence, given the premises, if the conclusions do not follow, the economic theory under consideration is said to be logically fallacious. This, in fact, happened to the marginalist theory of value and distribution. In the 1960s, it was demonstrated bySraffa,’Garegnani‘and others that marginalist theory of value and distribution is logically fallacious. This was shown so clearly that defenders of the theory, notably,’Paul Samuelson, admitted this defect. The main reason for this logical fallacy was/is that prices (value) and distribution are interdependent and hence are simultaneously determined. Therefore, the distribution theory in neoclassical economics (marginal productivity theory) cannot be logically prior and independent of the theory of prices (value). In other words, capital cannot be treated as a distinct factor of production, independent of prices. This is because, at an aggregate level, capital is comprehensible only as a value magnitude. Therefore, the construct of the aggregate production function breaks down and with it the whole neoclassical edifice of value and distribution crumbles. In any case, to circumvent such logical critiques, the concept of inter-temporal equilibrium was constructed. So far, it seems to have been ‘successful’ in warding off capital-theoretic critiques. But, this shift towards inter-temporal equilibrium from long period equilibrium has seriously compromised the relevance of such economic theory. For, ‘anything goes’ in temporary equilibrium. The capital theoretic fallacy is of the’non sequitur‘type as there is an insufficient link between the premises and conclusion.

Marginalist economics studies human behaviour. It is a science of choice thanks to Lionel Robbins who presented a clear definition of neoclassical economics (which originated in the works of Jevons, Walras and Menger in 1870s). Hence, the theory assumes scarcity of both factors and commodities. The central problem in economics becomes that of ‘ allocation. The theory starts with specifying endowments to agents and concludes’ that there is full employment of resources. After all, if the issue is that of allocation, there will necessarily be a full-employment of resources both before’and‘after the process of allocation (carried out by the market forces of demand and supply). In this case, the premises and the conclusion are connected in such an intimate manner that it seems to commit the fallacy of’petition principia.

Consumers maximize utility. Producers maximize profits. This gives us equilibrium. However, is there a clear line of demarcation between a producer and a consumer’ What if an agent is both a consumer and a producer’ In the language of set theory, what if the intersection between consumers and producers in an economy is not a null set’ If so, is it logically consistent to have a’strict‘demarcation between producers and consumers’

Logical fallacies in economic policy

Economists, policy makers and journalists argue for a particular economic policy based on certain premises. These premises are nothing but an admixture of various economic theories. Note the emphasis on ‘theories’, for there is not just one economic theory but multiple economic theories. Most of them are competing paradigms, i.e., they ask similar questions but provide dissimilar answers. Examples include Austrian economics, Marxian economics, Classical economics and Keynesian economics. The dominant paradigm, of course, is the marginalist one; variants of this include New Classical Macroeconomics, Monetarism, New Keynesian Macroeconomics, Microeconomics, etc.

The question we are interested in asking is: what is the basis on which a particular economic policy is favoured. A few examples are provided below.

I

Premise: Increase in money supply causes inflation.

Conclusion: Therefore, increase interest rates to reduce inflation.

II

Premise: Inflation is determined by inflation expectations.

Conclusion: Therefore, the Central Bank should target inflation expectations.

III

Premise: Given full-employment of all resources, an increase in expenditure will raise prices.

Conclusion: Fiscal deficits are inflationary. Therefore, reduce fiscal deficits.

The premise in the first example is from a Monetarist paradigm; the premise in the second one is a New Keynesian perspective and the premise in the third example is a typical neoclassical/marginalist view. Are these kinds of policy conclusions logically correct’ Do the conclusions follow from the premises’ Or, are we taking a leap of faith’ For, the economies which the premises talk about and describe aretheoretical worlds‘which (hopefully) have certain characteristics of the real-world. In any case, hasty conclusions should not be made. This is especially important for policy making in an economy like India which is very distinct from the theoretical worlds mentioned above.

Yet another commonly used argument is to favour a policy based on its success in another economy. For a long time, India followed economic doctrines which were promoted in the advanced economies of the West. Today, we see a similar trend where examples and case-studies from ‘other emerging economies’ are used to argue for a particular policy recommendation in India. But, India is structurally ‘ socially, culturally, politically and economically different from these other economies. Hence, we again take a leap of faith. I end with such a’claim which was made‘to argue that FDI is favourable: ‘in Indonesia 10 years after allowing 100 per cent FDI, 90 per cent of the retail sector is controlled by the small shopkeepers.’

Knut Wicksell: Some Aspects of his Work

This post is different from the others because it deals with the contributions of a single economist. Knut Wicksell was a Swedish economist who made significant contributions to capital theory, monetary economics and fiscal policy. Despite being grouped under the neoclassical or the Austrian school because of his affinities to ‘marginal’ analyst, Wicksell was a socialist and a radical. He advocated policies which involved the government in a big way. And owing to his varied interests in poetry, mathematics, feminism, mathematics, politics, etc he became a Professor of Economics and Fiscal Law at Lund University only when he was fifty. A few of his well known students are Erik Lindahl, Gunnar Myrdal and Bertil Ohlin. They are considered to be part of Stockholm or Swedish school of economic thought.

In the passages below, only a few of his contributions will be elaborated. He has also made lasting contributions to the theory of interest, revitalised quantity theory of money, introduced mechanisms linking the real and monetary sector, etc.

Wicksell demonstrated that problems could arise if capital is treated just like other ‘factors of production’ ‘ land and labour. Cambridge capital controversies dealt with many of these problems. ‘Knut Wicksell (1851’1926) himself casts doubt on the specification of the value of capital, along with the physical quantities of labour and land, as part of the data of the system. ‘Capital’ is but a set of heterogeneous capital goods. Therefore, unlike labour and land, which ‘are measured each in terms of its own technical unit . . . capital . . . is reckoned . . . as a sum of exchange value’ (Wicksell, 1901, 1934, p. 49). But capital goods are themselves produced commodities and, as such, their ‘costs of production include capital and interest’; thus, ‘to derive the value of capital goods from their own cost of production or reproduction’ would imply ‘arguing in a circle’ (ibid., p. 149).’ [Segura and Braun 2004]

Like other contemporaries of his, Wicksell did not write about unemployment. This was because the existence of unemployment was considered to be a paradox, an anomaly for neoclassical economists. As they could not comprehend why resources (here, labour) would be left idle! The central problem in (neoclassical) economics was not to provide or create uses for factors, but only to allocate the factors among various uses. As Bo Sandelin, editor of Wicksell’s papers and the author of A History of Swedish Economic Thought writes in the introduction that ‘the fundamental question in economics was how to manage an economy with scarce resources.’ Strange indeed!

Wicksell was a strong proponent of the marginal productivity theory of distribution. A corollary of this theory is the the sum of all the marginal products of the factors should be equal to the total product, known as the product exhaustion theorem. However Wicksell demonstrated that the operation of this theory depends on the returns to the scale. That is, only under constant returns to scale will the marginal products exactly add up to the total product. And that for both decreasing returns and increasing returns, the product will not be completely exhausted.

The Swedish school made another important contribution to economic theory. They introduced the categories of ex ante and ex post. These categories, we know are used widely today and were the result of the School’s dissatisfaction with the equilibrium analysis. Apart from these ways of thinking, Myrdal has provided us with the concept of circular and cumulative causation as well. These categories provide us with alternative modes of conceptualising or thinking about economic problems.

Relying solely on textbooks reduces our extent of reach. We often fail to come across interesting and heterodox economists. But, history of economic thought provides us with ample personalities to look into. Wicksell is one among them. Also, some of their categories provide us with alternatives, which remain unfinished. For instance, after going through some of the secondary and primary works on/by Wicksell, he appears exceedingly interesting and aware of the implications of certain simplifying assumptions. He pointed out the ‘necessity’ of the constant returns to scale assumption, which economics faithfully aligned with for a considerable period. This was challenged within the mainstream only with the entry of the endogenous growth theories, which emphasised increasing returns.

References

Pressman, Steven (2004), Fifty Great Economists, Routledge: India.

Groenewegen, P and Vaggi, G (2006), A Concise History of Economic Thought: From Mercantilism to Monetarism, Palgrave Macmillan.

De Marchi, N and Blaug, M (1991), Appraising Economic Theories: Studies in the Methodology of Scientific Research Programmes, Edward Elgar.

Segura, J and Braun, C (2004), An Eponymous Dictionary of Economics: A Guide to Laws and Theorems Named After Economists, Edward Elgar.