On Financial Markets: The Problematic Assumptions

More than half of the dissertations and theses in India are on financial markets. Various aspects such as pricing of options, efficiency of markets, volatility of markets, its impact on the real sector, futures markets, effect of foreign trade, etc are analysed. Financial markets refer to the stock market, the derivatives market, the commodity markets, etc. For our purposes, we will take into account only the stock/share market as it is the one that is most well-understood in comparison to the rest. This blog post echoes a lot of my concerns with the way financial markets are analysed, and also indicates some of the broader concerns about econometric work in general. I have been greatly motivated and moved by Benoit Mandelbrot’s and Richard Hudson’s book The (Mis)Behaviour of Markets in writing this post. All quotations in this post are from their book.

On attending several pre-submission, post-submission, work-in-progress and viva-voce seminars, I have often wondered about economists fascination with the ‘normality assumption’. We assume that price changes follow a normal distribution, that is, outliers (both small and large) do not significantly affect the average/expected value. That is, standard theories of finance ‘assume the easier, mild form of randomness. Overwhelming evidence shows markets are far wilder, and scarier, than that.’ Now, in natural sciences, this is a common enough assumption. Is there any empirical evidence supporting the use of such a distribution in economics, mainly the analysis of changes in prices and quantities’ One wonders. In fact, it is this distribution which underlies the most commonly used tool in regression ‘ the method of least squares. Most studies (academic and corporate) measure volatility using variance or standard deviation of the normally distributed variables. As Mandelbrot asks, ‘is this the only way to look at the world”

Apart from the normality assumption, orthodox financial theory makes the following assumptions. This list is directly based on Mandelbrot’s book. (1) People are rational and aim only to get rich. (2) All investors are alike and they are price-takers, not makers. (3) Price change is practically continuous. (4) Price changes follow a Brownian motion, that is each price change appears independently from the last, the price changes are statistically stationary and that the price changes are normally distributed.

Assumptions (1) and (2) need no discussion, owing to their obvious falsity. Now it is assumption (3) that allows the use of continuous and differential functions; whereas, the reality is that ‘prices do jump, both trivially and significantly’ and that discontinuity is an ‘essential ingredient of the market.’ The meaning of independent price changes is that, price at t+1 is not dependent on price at t. In other words, prices have no memory. An example from tossing a fair coin will illustrate this better. Suppose a fair coin is tossed once, we get a head. The outcome of the next toss is not based on the outcome of the previous one. Again, how true this is of stock markets or of prices is questionable. How can such an assumption cope up with ‘expectations’ of investors’ The statistical stationarity of price changes implies that the process generating the price changes stays the same over time.

Very often, in research, we do not have the time to question these assumption; not only that, these assumptions function as received wisdom. However, as Mandelbrot comments, ‘They work around, rather than build from and explain, the contradictory evidence’ because ‘It gives a comforting impression of precision and competence.’ For, a high kurtosis (the measure of how closely the data fits the bell curve) has been found in the prices of commodities, stocks and currencies.

To conclude, how does one as a researcher overcome such problematic/unreal/easy assumptions’ Is this what academic ‘discipline’ means’ Or are we to learn adequate mathematics and statistics so that we can find a way around it’ Or do we cooperate and seek help from mathematicians and statisticians’ Mandelbrot has developed tools and concepts such as ‘fractal analysis’ and ‘long memory’ which can aid economics, which is inherently not a study of normally distributed variables.

Sraffa: The Origins of ‘Marginal’ Analysis

Since the advent of the ‘marginal’ method, the doctrines of the old classical economists have been submerged and forgotten. It is this standpoint that Sraffa revives in his 1960 book Production of Commodities by Means of Commodities. Being third in the series of posts [Post 1; Post 2] on Sraffa, this post examines the origin of the ‘marginal’ method and its subsequent (mis)use by the neoclassical economists. The posts concludes with a brief mention of how history of economic thought is important so as to place theories in a proper context.

In the preface of his book, Sraffa points out that in a system of production where the scale of an industry or proportions of factors of production remained unchanged, one would not be able to locate marginal product and marginal cost. To put it differently, marginal analysis is done by considering ‘potential change’. That is, we try to find out variations in equilibrium quantities and prices with respect to infinitesimal changes in the neighbourhood. [Bharadwaj 1986, p 39]

What we do not pay adequate attention to, is that the most familiar case of ‘marginal analysis’ is that of the product of marginal land (also known as no rent land) in agriculture, when lands of different qualities are cultivated side by side. This refers to the well known differential rent theory of David Ricardo. In fact, it is the case of diminishing marginal returns on land which is at the junction of the ‘fundamental methodological shift from classical to equilibrium theory’. [Bharadwaj 1986, p 40] This can be understood only through a discussion of ‘extensive’ and ‘intensive’ margins.

Cultivation on lands of different qualities is visualised as the outcome of a process of ‘extensive’ diminishing returns. On the other hand, successive use of more output producing techniques refers to the process of ‘intensive’ diminishing returns. [Sraffa 1960, p 76] In the case of ‘extensive’ margins in cultivation, ‘the rents can directly worked out on the basis of the single observed situation.’ [Bharadwaj 1986, p 41] Whereas, in the case of ‘intensive’ margins, the calculation of rent requires a quantitative change in the situation. That is, successive doses of labour and ‘capital’ need to be added to the land. And, a further assumption is made on the nature of these ‘doses’. These ‘doses’ are considered to be homogeneous. As Krishna Bharwadwaj explains: ‘At any moment of observation, no dose is distinguishable from each other. No ‘marginal product’ can, therefore, exist in this case without introducing potential change.’ [Bharadwaj 1986, p 42]

Thus, it is the Ricardian theory of rent which provided the basis for the neoclassical theory of distribution by providing an inverse relationship between successive doses of labour and ‘capital’ and their remuneration. This theory of Ricardo was intended to explain the origin of rents. In the hands of later authors, this was generalised to labour and ‘capital’. Hence, we see the inverse relation between ‘capital intensity’ and rate of profit in microeconomics textbooks of today.

From this excursion into the Ricardian theory of rent, two aspects are very clear. First, the concept of ‘marginal’ or ‘margins’ was used exclusively in the domain of cultivation. In ‘intensive’ cultivation, it is obvious that the output would increase only until a certain point, owing to the quality of that piece of land. Whereas, in the case of ‘extensive’ cultivation, the output would increase till all the acres of land are cultivated- notice the scarcity element here. What is not clear is the rationale of extending such an analysis into the area of manufacturing! Also, it is well accepted that land is scarce; but, is ‘capital’ or produced commodities scarce in a similar way’

No book of microeconomics mentions the origins of the famous ‘marginal’ analysis. And this method is so entrenched in the profession, that it is almost impossible to throw it away. It is in this context that other conceptual frameworks, that pay more attention to the changing historical conditions, assume importance. Probably, we need to revisit earlier theories and theorists not just for their own sake but for our sake as well in throwing light on contemporary issues. Sraffa’s work has inspired a lot of work on the history of economic thought, which will be summarised in a later post.

References

Bharadwaj, Krishna (1986), ‘Classical Political Economy and Rise to Dominance of Supply and Demand Theories‘, Universities Press: Calcutta.

Sraffa, Piero (1960), ‘Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory‘, Cambridge University Press: Cambridge.

Model Building and Planning in India

Ever since the First Five Year Plan, we have utilised models in order to channel resources for achieving objectives of higher growth, establishing strong capital base, strengthening import substitution, reducing poverty, increasing foreign exchange resources and so on. The early plans made use of Harrod-Domar model and the Feldman-Mahalanobis models. The models used for planning purposes were largely taken from economic theory, which were then adapted (hopefully) by the Planning Commission. Owing to changes in the structure of the Indian economy, the nature of modelling has also undergone various alterations. This post highlights certain issues in the macro-modelling that was done for the 11th Five Year Plan, chiefly based on the publication by the Planning Commission Macro-Modelling for the Eleventh Five Year Plan of India edited by Kirit S Parikh.

It is incorrect to argue that planning in India has become redundant after the 1991 reforms. These reforms provided freedom to the firms with respect to what to produce and how to produce them. As the recent global financial crisis has shown, unregulated finance can lead to unfavourable outcomes for the financial as well as the real sectors of the economy. Also, significant divergences in income and wealth are being reported. This is the case, especially in India which is home to some of the richest and poorest people in the world. As Parikh writes, ‘As long as disparities in income, endowments and wealth persist, access to public goods and services is uneven and infrastructure paucity is there, we need active government policy. We need planning.’ [Planning Commission 2009, 16]

The 11th Five Year Plan’s goal is to have ‘Faster and More Inclusive Growth’. The basis of this goal is that the growth of GDP is treated as a necessary and almost sufficient condition for improving livelihoods. We know that markets exclude those without adequate purchasing power. And growth in GDP mainly results in an increase in the extent/size of the market. Unless appropriate systems are in place, ‘trickle down’ does not take place. Hence, an outline of how ‘inclusive growth’ can take place needs much greater attention. And it is disappointing to see that employment generation is not considered as a central objective. For the first time, the inputs of the 11th Five Year Plan have been provided by a ‘modelling forum’. The forum consists of researchers from NCAER, IGIDR, IEG and ISI Bangalore apart from the in-house team of the Planning Commission.

A formal model is constructed for the purposes of planning because it makes the assumptions transparent, ensures consistency and provides insights into the inter-relationship between various actors and sectors in the economy. These models in turn borrow concepts, categories, functional relationships and links from the paradigms in economics. The paradigms that have influenced modellers, according to Parikh are Input-Output, Walrasian, Neoclassical, Keynesian, Structuralist, Vector Auto Regression/Error Correction, New Neoclassical and Dynamic Stochastic General Equilibrium. The most obvious drawback of this classification is the mix-up of paradigms with tools of economics. For instance, IO framework, VAR models and DSGE models are only tools. For our later exposition, it would be helpful to point out the important characteristics of each of these paradigms/tools.

Input-Output: Usage of inputs in fixed proportion

Walrasian: Optimising behaviour of economic agents

Neoclassical: Pricing through supply and demand mechanism and full employment at prevailing wage rate

Keynesian: Underemployment equilibrium

Structuralist: Imperfect markets and incomplete monetization of the economy

Vector Auto Regression: All variables depend on lagged values of all variables and data speak for themselves

New Neoclassical: Microeconomic foundation of macroeconomics- importance of information, expectations and contracts

DSGE: Forward looking and optimising economic agents

In the modelling for the 11th Five Year Plan, six different models with different analytical approaches have been used. The models are a) Perspective Planning Division’s In-house Model, b) A VAR/VEC Model from ISI, Bangalore, c) A General Equilibrium Model from IGIDR, d) An Econometric Model from IEG and e) Macro-Econometric Model of NCAER. The various model scenarios show that the direction of policy shocks are similar ‘though the structure and philosophy of the models are different’. However, this is not such a shocking or an interesting revelation. For everybody knows that oil price shocks have a negative impact on the GDP growth rate and that the global slowdown affects the GDP adversely. The only result of interest is that of an increase in NREGs by 1% of GDP. This will result in an increase of around 0.35 to 0.5 GDP percentage points. However, it must be noted that this is based on ‘a general equilibrium model in which it is assumed that the adjustments to the new equilibrium are completed in one year. Thus, the impacts may be overstated as in reality this may not be the case’.

Overall, it seems that the assumptions of the various models are far from our Indian reality. There is no attempt at including the unorganised sector. And it is very clear, from the recent evidences from neuroeconomics, experimental economics and game theory that individuals are not rational optimizing machines. Instead, we are more moved by social concerns and we exhibit a pro-social behaviour which is norm-based. There is no explicit move to analyse employment generation. Nor is there the necessary focus on agriculture. It is stated that agriculture needs to grow by 2.4 % to 4 % so as to achieve 9% GDP growth rate. One cannot help but wonder whether the objective of economic planning in India is only about the GDP growth rate! And as to the use of VAR models, the generators of the model argue that since there is ‘no real basis to say which variable is endogenous and which is exogenous’, they adopt a ‘general equilibrium approach, where everything (except rainfall, of course) depends on everything else.’ [Planning Commission 2009, 88] An easy route indeed!

This publication by the Planning Commission is a must read for all those who are interested in understanding the Indian policy making. Also, it provides the crucial link between policy and theory. Hence, making the study of economic theory very significant, especially for policy makers. It will also be of interest to students and practitioners of time series methods using the VAR framework.

Reference

Planning Commission (2009), Macro-Modelling for the Eleventh Five Year Plan of India, edited by Kirit S Parikh, Academic Foundation: New Delhi.

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.