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.

60 Years after the 2nd Five-Year Plan: On Economic Theory, Planning & Policy

Picking up Ajit Dasgupta’s A History of Indian Economic Thought (1993) motivated me to revisit India’s 2^nd Five Year plan (1956-61) and the Mahalanobis model in light of the structural changes in India’s economy and developments in economic theory, particularly of demand-led growth theory. Although 60 years have passed since the inception of the 2^nd Five Year plan, the ‘Approach to the Second Five Year Plan’ contains ideas which are particularly important today, especially after the closure of the Planning Commission. In its place, we now have the NITI (National Institution for Transforming India) Aayog which assumes that Indian manufacturing and service sectors are currently operating ‘on a global scale’ and what is now needed is ‘an administration paradigm in which the government is an “enabler” rather than a “provider of first and last resort”‘ (see Cabinet Secretariat resolution, 1 January 2015).

Why economics’

Economics is the study of commodities ‘ its production, distribution and consumption. Economics provides us with the determinants of aggregate production (GDP), employment, and income distribution. This allows us to understand our economic surroundings better and consequently enables us to improve existing economic conditions. This may be carried out through general economic policies (for example, progressive taxation to reduce income and wealth inequalities and monetary policy to combat inflation) or through targeted economic policies (for example, fertilizer subsidies to improve agricultural productivity and tax concessions to foreign investors). Ultimately, economic interventions are made based on an assumption and several aims. The assumption is that economic theory tells us how economies function. The interventions are carried out to satisfy certain normative aims (for example, equity and freedom). This distinction is made in textbooks by distinguishing between positive and normative economics. For instance, if a particular society is not uncomfortable with unemployment its economic policies would not be aimed at reducing unemployment.

Objectives of the 2nd Five Year Plan

In this section, the economic objectives of the 2^nd Five Year Plan are presented. All excerpts from the 2^nd Five Year Plan are taken from here.

‘The current levels of living in India are very low. Production is insufficient even for satisfying the minimum essential needs of the population’.’ Therefore, it was imperative to increase aggregate production. But, the economic architects of the plan did not visualize money as an end in itself.

‘A rising standard of life, or material welfare as it is sometimes called, is of course not an end in itself. Essentially, it is a means to a better intellectual and cultural life. A society which has to devote the bulk of its working force or its working hours to the production of the bare wherewithals of life is to that extent limited in its pursuit of higher ends.’

Moreover, economic policy was aimed at an increase in activity levels and ‘also in greater equality in incomes and wealth.’

The Plan Document clearly favours social gain over private gain. In other words, private enterprise was regulated such that the economic yields benefitted all. To put it differently, a recognition of negative externalities was present.

‘The private sector has to play its part within the framework of the comprehensive plan accepted by the community. ‘ Private enterprise, free pricing, private management are all devices to further what are truly social ends; they can only be justified in terms of social results.’

More clearly,

‘Economic objectives cannot be divorced from social objectives and means and objectives go together. It is only in the context of a plan which satisfies the legitimate urges of the people that a democratic society can put forward its best effort.’

The Plan Document also recognized the dual nature of urbanization ‘ that economies of scale have both positive economic externalities and negative environmental externalities.

The 2nd Five Year Plan on economic inequality

The 2^nd Five Year Plan clearly recognized that the gains from economic development are skewed and trickle down is not automatic. For the gains from economic development to be inclusive, two institutions have to be strong: trade unions and the democratic state.

‘The gains of development accrue in the early stages to a small class of businessmen and manufacturers, whereas the immediate impact of the application of new techniques in agriculture and in traditional industry has often meant growing unemployment or under-employment among large numbers of people. In course of time this trend gets corrected partly through the development of countervailing power of trade unions and partly through state action undertaken in response to the growth of democratic ideas.’

There is a passage similar to Thomas Piketty’s view on wealth inequalities and the role of progressive taxation in reducing such inequalities in the document.

‘The most important single factor responsible for inequalities of income and wealth is the ownership of property. Incomes from work are by no means equal, but in part at any rate, they have some justification in terms of productivity or relative scarcity. Some types of work are, however, remunerated more liberally than others for reasons which are not directly connected with productivity. Differential monetary rewards are often a matter of tradition an existing psychological or social rigidities. It has also to be borne in mind that capacity to work effectively at higher levels depends on a person’s education and training, and these are a matter of the accident of birth or circumstances. A large expansion of general and technical education for all classes of people irrespective of their paying capacity is over a period a potent equaliser. The point is that while inequalities in incomes from work have to be corrected, the case for taxation based specifically on wealth or property needs to be carefully examined.’

India needs to seriously consider a tax on wealth given the wide disparities of income and wealth. The connection between ‘productivity’ and ‘social rigidities’ is noteworthy and requires to be addressed through labour laws, education policy, food policy, employment policy and so on.

The core of the 2nd Five Year Plan: the Mahalanobis model

From the previous paragraphs, we can state the following as the normative economic aims of the 2^nd Five Year Plan: (1) expansion of output and employment opportunities, (2) reduction of income inequalities, and (3) inclusive economic growth and development. The economic core of the 2^nd Five Year Plan is constituted by the Mahalanobis model. As Ajit Dasgupta writes in A History of Indian Economic Thought, ‘The purpose of the model was to determine the optimal allocation of investment between different productive sectors so as to maximise long-run economic growth in India’ (p. 164). In other words, the aim of this model is to increase the pace of aggregate economic activity in India.

The Mahalanobis model is a two-sector model with a capital goods and a consumption goods sector. The model tells us how the resources are to be distributed between these two sectors such that maximum economic growth is achieved. Note that the then production was insufficient to meet the basic needs of the Indian populace. There are inter-sectoral relations due to which one sector cannot exist (or grow) without the other. To produce consumption goods, capital goods are required. For the workers and capitalists in both sectors, consumption goods are needed. Employing the Mahalanobis model is to some extent vindicated because the model assumes ‘capital to be the effective constraint on output’ and India lacked good physical infrastructure.

Note also that this model assumes that there are no demand constraints. As Dasgupta writes, ‘The higher the proportion of investment (i.e. of the current output of capital goods) that is allocated to the further production of capital goods, the higher the long-run growth rate of output’ (p. 165). The dual character of investment is not clearly understood for investment creates productive capacity and is a component of aggregate demand. Logically, a solution can be found such that the addition to capacity is validated by the demand generated but it is a knife-edge equilibrium as in Harrod.

Dasgupta points out that the Mahalanobis model has been criticized ‘for being concerned exclusively with investment and for identifying investment with the production of capital goods’ (p. 165). Yes, demand constraints and human capital investment are ignored. Another criticism of the model has been its neglect of foreign trade (p. 166). However, the model could be modified easily to account for foreign investment and consumption whereas the incorporation of demand constrains and human capital would not be easy.

Conclusion: the relevance of economic planning

Since the 2^nd Five Year Plan, much time has passed and the Indian economy has undergone several changes. Developments have taken place in economic theory too, particularly in the areas of economic growth and development. While the Mahalanobis model has its limitations, the normative aims of the 2^nd Five Year Plan are still valuable today. The expansion of employment opportunities needs to be at the forefront of any macroeconomic or growth strategy. As written in the 2^nd Five Year Plan, ‘From the economic as well as from the larger social view point, expansion of employment opportunities is an objective which claims high priority’. However, NITI Aayog, the successor to the Planning Commission works within ‘an administration paradigm in which the government is an “enabler” rather than a “provider of first and last resort”‘. The market cannot be expected to provide accessible and good quality education, health, housing and living environments to all. With existing economic and social inequalities, the need for economic planning is even more. Social costs require to be assessed and not ignored in the name of economic efficiency and economic growth.

An economic planner ought to know the implicit assumptions and scope of economic theories and be knowledgeable about legal and institutional constraints of policy implementation. The economic planner must therefore be an excellent economist and an experienced bureaucrat.