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.