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+…+k_np_n=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.

Frank Ramsey and the Rate of Interest

I first came across Frank Ramsey in the preface to Piero Sraffa’s classic Production of Commodities by the Means of Commodities: Prelude to a Critique of Economic Theory (1960). My recent interest in Ramsey is primarily motivated by the following news. Cheryl Misak, a philosopher based at the University of Toronto has recently completed a biography of Ramsey. This blog post provides an introduction to Ramsey’s life and his contribution to the growth theory literature. [It was reassuring to notice that I first blogged about History of Economic Thought (HET) explicitly more than 10 years ago.]

Ramsey was born in 1903. In the year 1920, he read around 45 books, which included Karl Marx’s Capital, Sidney Webb and Beatrice Webb’s The History of Trade Unionism, J. A. Hobson’s The Industrial System, J. S. MiIl, and Alfred Marshall’s Industry and Trade. At the age of 19, he was commissioned to review Ludwig Wittgenstein’s Tractacus Logico-Philosophicus (1922), a significant treatise in philosophy, for the journal Mind; the review was published in 1923. Subsequently, he was commissioned to translate Wittgenstein’s work into English. In Wittgenstein’s later work, Philosophical Investigations, there is an explicit acknowledgement of Ramsey. He was acknowledged for his critique/interventions of Bertrand Russell’s and Alfred Whitehead’s Principia Mathematica in a new introduction by the authors. Sraffa, in his PCMC, had acknowledged Ramsey for mathematical help. In 1929-30, Ramsey met with J. M. Keynes, Sraffa, and Wittgenstein to discuss the theory of probability advanced by Keynes and Ramsey and also to discuss Freidrich Hayek’s theory of business cycles. Ramsey also had a close engagement with AC Pigou, a leading marginalist economist who was also the target of criticism in Keynes’s General Theory. Ramsey died in 1930.’

Under the patronage of Keynes, who was the editor of the’ Economic Journal, Ramsey published in it articles on the ‘theory of taxation’ (1927) and the ‘theory of saving’ (1928). In my 2019 article which critically evaluated the Nobel contributions of Paul Romer and Nordhaus, I had highlighted that Nordhaus employs a marginalist growth model drawing from Ramsey (without further comment). Ramsey’s question was the following: how much should a nation save today for future consumption tomorrow so as to maximise consumption across generations’ Nordhaus employs the optimal growth model with environmental protection as an important constraint. And, the rate of interest is seen as a price which equilibrates the society’s time preference. In other words, the rate of interest equilibrates the society’s preference for the future with that of the present. The policy implication when marginalist economists have a significant say in practical matters is as follows. Since the (actual) rate of interest captures the time preference of the society, this rate can be used to decide how much of current gross domestic product (GDP) should be devoted to environmental protection. In effect, not enough resources are being allocated to mitigate climate change and undertake environmental protection.’

Ramsey’s optimal growth theory also underlies Thomas Piketty’s position on economic growth. In his 2015 article in the American Economic Review, he writes that in the standard model ‘where each individual behaves as an infinitely lived family, the steady-state rate of return is well known to be given by the modified ‘golden rule’ r = ‘ + ‘ g (where ‘ is the rate of time preference and ‘ is the curvature of the utility function)’ (p. 2). The reciprocal of ‘ is the intertemporal elasticity of substitution which captures how much the representative family wishes to smoothen consumption over time. He uses this to point out that in general (marginalist) economic theory, we arrive at the r>g result–the focal argument in his book Capital in the Twenty First Century (2015; for a critical assessment see Thomas 2017). Furthermore, ‘in steady-state each family only needs to reinvest a fraction g/r of its capital income in order to ensure that its capital stock will grow at the same rate g as the size of the economy, and the family can then consume a fraction 1 ‘ g/r‘ (p. 3). To a marginalist (or neoclassical) economist, as Joseph Stiglitz wrote in an article in 1974, ‘interest rates are just intertemporal prices’ (p. 901).’

Therefore, for both Nordhaus and Piketty, interest rates are ‘intertemporal prices’ which allocate today’s income between today’s consumption and tomorrow’s consumption (today’s saving). As Ramsey (1928) writes, ‘The more we save the sooner we shall reach bliss, but the less enjoyment we shall have now, and we have to set the one against the other’ (p. 545). It is also interesting to note that their use of optimal growth models yields vastly different policy suggestions. While Nordhaus is conservative in his proposals for environmental protection, Piketty is progressive in his proposals to tax wealth.’

The rate of interest in Ramsey, as in Alfred Marshall, is a reward for waiting. Therefore, inequality in Ramsey necessarily arises from the heterogeneity of tastes or preferences; if a family is (relatively) more patient, it saves more than the (relatively) impatient one, and ends up owning all the capital stock (Attanasio 2015). How does this conception differ from the notions of interest rate found in Marx and Keynes’ For Marx, the rate of interest is the part of surplus value which is expropriated by the financial capitalist; the source of it is from the value added by labour. Keynes views the rate of interest as an expression of the preference for liquidity. To conclude, is the conception of the rate of interest found in Ramsey satisfactory for understanding a competitive economy’

REFERENCES

Attanasio, Orazio P.’ (2015), ‘Frank Ramsey’s Mathematical Theory of Saving’, The Economic Journal, 125 (March), pp. 269’294. https://doi.org/10.1111/ecoj.12229

Duarte, Pedro (2017), ‘Frank Ramsey’, In: Robert Cord (ed.) The Palgrave Companion to Cambridge Economics, Palgrave Macmillan, vol. 2, pp. 649’671.

Monk, Ray (1990), Ludwig Wittgenstein: The Duty of Genius, London: Vintage Books.’

Stiglitz, Joseph E. (1974), ‘The Cambridge-Cambridge Controversy in the Theory of Capital; A View from New Haven: A Review Article,’ Journal of Political Economy, vol. 82, no. 4, pp.’ 893‘903.

Further reading

Collard, David (2011), ‘Ramsey, saving and the generations’, Generations of Economists, London: Routledge.’

[Most of the contents of this post was informally discussed with my Economics colleagues at Azim Premji University on 19th February 2020.]

The Union Budget 2018-19 in 5 charts

The Union Budget is a key document which informs the public about the Government’s socio-economic plans and priorities. It is important to critically evaluate this document because of our collective ‘failure to provide for full employment’ and the ‘arbitrary and inequitable distribution of wealth and incomes’; Keynes wrote this in 1936 and it continues to remain the same. Moreover, it is our collective right and responsibility to decide how the government should obtain its revenue and how it must be spent. No formula or algorithm exists for this. As Piketty wrote in his Capital in the Twenty-First Century, ‘Taxation is not a technical matter. It is preeminently a political and philosophical issue, perhaps the most important of all political issues. Without taxes, society has no common destiny, and collective action is impossible.

This blog post aims to outline the priorities of the current central government by examining the expenditure on physical and social infrastructure and the nature of taxes. This is done in 5 charts.

(1) Physical Infrastructure

Defence is significantly more important than roads, housing, food, and farmers’ welfare.

Capital Expenditure of Select Central Ministries (in Rs. Crore)

Source: Expenditure Budget Vol. 1, 2016-17, Statement 2, pp 4-9

All values are rounded off to the nearest crore.

(2) Social Infrastructure

Physical infrastructure creation is more important than social infrastructure creation.

Have the negative effects of physical infrastructure creation been accounted for’

‘Total Allocations of Select Ministries (Rs. 112753 Crore)

Source: BS, p 36, Annex No. III-A to Part A

RE refers to revised estimates which include supplementary demands for funds made by the ministries during the financial year.

BE refers to budget estimates.

(3) Direct & Indirect Taxes

Our taxation policy is regressive due to the high proportion of indirect taxes.

Select Direct and Indirect Taxes (in Rs. Crore)

Source: Receipts Budget, 2018-2019, pp. 2-4

(4) Corporate Tax Concessions

Our tax concessions could approximately fund 75% of the social infrastructure spending estimate.

(5) Corporate Tax Structure

Our corporate taxes are regressive.

Effective tax rate paid by sample companies across range of PBT (FY 2016-17)

Source: Statement of Revenue Impact of Tax Incentives under the Central Tax System: Financial Years 2014-15 and 2015-16, p 30 of the Receipts Budget, 2016-2017, Annex-15.

¹ Values rounded off to the nearest integer; hence the total adds up to 101 and not 100. Financial year 2012-13. The number of companies whose PBT is zero is 17,912 and their share in total income is around 9 per cent.

Concluding comments

Our government prioritises defence over agriculture. Our government prioritises physical infrastructure over social infrastructure and does not take into account ecological damage and the displacement caused due to physical infrastructure creation. And our taxation policy is regressive. We must use our collective rights and responsibilities to decide how the government should obtain its revenue and how it must be spent.

Acknowledgement

I thank Rahul Lahoti for inviting me to be a part of the panel which discussed the Union Budget at Azim Premji University-Undergraduate Campus on 14th February 2018, from which this post originated.

On free individual choice and collective inaction

The logic of contemporary economies is built on our belief in the virtues of ‘free’ individual choice. Adherents of this view, which include (most) governments, corporations and many individuals, believe that regulating individual choice is bad for the economy. However, among this syndicate, some do recognise the pitfalls of employing this principle in the development and growth of institutions relating to education and health. In economic parlance, the ‘failure’ of individual choice in yielding a socially beneficial outcome is termed a market failure ‘ suggesting that markets, in general, do not fail. It is important to state the logic of individual choice explicitly owing to its enthralling grip over contemporary political and economic imagination. John Maynard Keynes in his 1926 critical essay ‘The End of Laissez-Faire’ makes explicit this logic: ‘by the working of natural laws individuals pursuing their own interests with enlightenment, in condition of freedom, always tend to promote the general interest at the same time!‘

How did private vice transform into private interest (and choice)’ And how is it that private choice is at the core of today’s economics and politics’ Albert Hirschman’s The Passions and Interests:Political Arguments for Capitalism Before its Triumph (1977) provides us with one compelling historical account. The idea that free individual choice results in socially beneficial outcomes is now commonplace. This was not always the case. In fact, Montesquieu, the French philosopher, wrote about the socially beneficial outcomes from pursuing honour which ‘brings life to all the parts of the body politic’ and ‘it turns out that everyone contributes to the general welfare while thinking that he works for his own interests.‘ By the seventeenth century, it was recognised that the ‘disruptive passions of men’ could not be restrained by moral philosophers and their religious counterparts although attempts to convert the disruptive passions into ‘constructive’ passions were already underway. For instance, anticipating Adam Smith, Pascal, another French philosopher, writes that man ‘has managed to tease out of concupiscence an admirable arrangement’ and ‘so beautiful an order.’ Subsequently, the idea of ‘countervailing passions’ started gaining currency in political thought. However, as Hirschman also notes, what forces actually ensure that groups (of individuals) with conflicting passions/interests result in a gain for all‘ If the contemporary politics of climate change is taken as an example, the outcome runs contrary to such an expectation.

Today, the widespread belief especially among policy makers is that unregulated individual choices ‘ whether as a consumer or a producer ‘ will ensure that the fruits of economic growth trickle down to the poorest person. However as Keynes warned us very persuasively in The General Theory of Employment, Interest and Money (1936), this belief is flawed and we need government intervention so as to eliminate labour unemployment. Clearly, the pursuit of individual gains has not brought social gains. Mainstream economics accommodates this big flaw in marginalist economics under the label of externalities. Unintended consequences of economic actions may be positive or negative for the society. In the determination of output and employment, Keynes pointed out that the tendency towards full employment (a more modest claim than public interest or social welfare) is a fluke in liberal capitalism. To put it differently, unemployment of labour is the expected consequence in liberal capitalism.Both theoretically and empirically, all evidence points to one inescapable fact: liberal capitalism does not result in the full employment of labour. Another charge by Keynes against this view is that it commits the fallacy of composition: what is good for an individual may not be good for the society. For example, while saving is good for an individual, if all individuals in a society save, who will consume the output’

Amitav Ghosh in The Great Derangement: Climate Change and the Unthinkable (2016), his recent* work of non-fiction, forcefully argues that the paralysis of climate change politics lies in our idea of individual freedom; our ‘calculus of liberty’ has no place for nature and natural systems. How then can our idea of freedom – a product of Enlightenment thinking ‘ and its close relative, democracy, ever effectively address our environmental issues’ A solution to our environmental problems warrants collective and concerted action. This is consistently absent in current politics, which has been reduced to individual morals and choices. Indeed, the onus of resisting environmental degradation has been passed on to the individual by appealing to her morals. As Ghosh puts it in his The Great Derangement, ‘This then is the paradox and the price of conceiving of fiction and politics in terms of individual moral adventures: it negates possibility itself.‘ Both fiction and politics, at their core, are, or rather, ought to be about possibilities ‘possibilities for the individual as well as the society as a whole.

The idea that free pursuit of individual interest yields a socially beneficial outcome is a flawed piece of political and economic imagination. Unfortunately, this principle does not function in today’s capitalist societies and the belief that it does is a dangerous one to safeguard. The idea that free individual choices yield socially beneficial outcomes must therefore be challenged in all possible spaces committed to documenting and exploring socioeconomic possibilities, particularly in humanities, journalism, literature, and the social sciences.

*I thank Vivek Nenmini for pointing out an error. Earlier, I had written that The Great Derangement is Ghosh’s first work of non-fiction.