Non-existence of objective probability distributions, Microeconomics

Non-existence of Objective Probability Distributions:

 

Let us see why expectations are volatile in nature? According to Keynes (1936, pp. 149): "Our knowledge of the factors which will govern the yield of an investment some years hence is usually very slight and often negligible." We can consider several examples:

i) possible advances in production technology might make the currently installed machinery obsolete,

ii) appearance of new substitutes might affect demand for output,

iii) changes in industrial, labour, trade and tax policies might affect revenues and costs,

iv) wars, trade embargoes and changing international relations might affect possibilities of production and sale. One can, with a fair degree of accuracy, predict the possibility of such events in the short term. However, such prediction becomes progressively more difficult, the farther ahead in the future is the time that such predictions relate to.

Such problems will, of course arise in making any decision about the future which involves long-term expectations. One possible way of dealing with such problems is to use a probability distribution over possible future outcomes. Keynes argued that in the case of variables like the future yields of an investment project there can be no objective basis for the formation of a probability distribution.

Let us explain the problem of forming a probability distribution through an example. Suppose we have to find out the outcome ('head' or 'tail') of a single toss of a coin in the future. We can repeatedly toss the same coin and observe outcomes. Alternatively we can consider past experience of coin tosses for coins with almost identical physical properties. In this way, we can obtain relative frequencies of the outcomes ('head' and 'tail') in the case of these tosses.

What are the factors presumably affecting the outcome of a single toss? Broadly, these are the nature of the coin, the method of the toss and the physical environment in which the toss is carried out. Certain factors can be broadly compared across different tosses and kept constant (so that only tosses under essentially similar conditions are studied), viz., the nature of the coin and the method of the toss. Other factors which might presumably affect the outcome are the exact initial position of the coin and the hand tossing the coin, the exact initial impetus given to the coin, the exact velocity of the wind blowing at the time the coin is tossed, and certain other factors in the physical environment. All these minute details may matter, but there is no way in which we can measure all these factors or keep them constant. For a particular coin the outcome (that is, obtaining 'head' or 'tail') depends upon the configuration of these factors.

However, suppose we compare sufficiently long sequences of coin tosses carried out' under essentially similar conditions. Depending upon the configuration of these factors we can represent a sequence of coin tosses in the form of relative frequencies for the outcomes. It implies that given a combination of factors the proportion of and 'tail' in a long sequence should remain the same.

In fact, it has often been empirically verified that for a sufficiently large number of tosses of a coin under essentially similar conditions, the relative frequencies of different outcomes tend to stabilise around fixed values. For example, for coins whose physical properties do not in any way appear to favour one outcome over the other, the relative frequency of the outcomes 'head' and 'tail' would both tend towards the value %.'These long-run relative frequencies then represent the objective basis for the probabilities assigned to different outcomes for a single toss of the coin in future.

Now, let us consider the case of an investment project. Certain pieces of information relating to past and present time periods are currently available which are relevant for forecasting possible future trends - for example, current yields on similar projects, past and current trends in these yields, current trends in science and technology (research and development) in related areas, current political developments and past political history. These, together with the nature of the investment project, can be considered as the observable conditions under which the experiment of investing in a project rather than tossing a coin is being made.

Unlike the case of coin tossing, we cannot undertake an investment project repeatedly and study the distribution of relative frequencies by outcomes. Therefore, one can only obtain this distribution by studying instances in the past where essentially similar conditions had prevailed. However, according to Keynes, there would be a very large number of pieces of information available at present, which could be considered relevant for predicting the long-run yields on any investment project. However, not all of these pieces of information are adequately quantifiable or comparable over time. Therefore, it is difficult to obtain sufficiently large numbers of instances in the past where investments have been made under essentially similar conditions.

Alternatively, suppose we wanted to use a limited number of quantifiable factors in defining the conditions under which investment is being carried out. In this case there is no reason why, if we consider sufficiently long sequences of these instances, it should necessarily be true that the distribution of relative frequencies of different configurations of the factors left out should be the same for all sequences. Science and technology or politics (human or social phenomena) are hardly of the same nature as physical (natural) phenomena. Consequently relative frequencies in the past might not be a good guide to relative frequencies in the future. 

 

 

Posted Date: 11/19/2012 7:09:42 AM | Location : United States







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