Most economists consider the use of sophisticated mathematical and statistical methods key towards understanding the complexities of economics. They are of the view that in order to be scientific, economics should follow in the footsteps of natural sciences.

By means of mathematical and statistical methods, an economist establishes relationships between various variables. For example, personal consumer outlays are related to personal disposable income and interest rates. Most economists presenting this relation as a mathematical function,

C=a*Yd – b*i

where C is personal consumer outlays, Yd is personal disposable income, i stands for interest rate, a and b are parameters. For instance, if a is **0.5**, b is minus **0.1**, Yd is **1000** and i the interest rate is **2**% then C will be **0.5*****1000** – **0.1*****2** =**499.8**.

Note that the parameters a and b are obtained by means of sophisticated statistical method called the regression analysis. By presenting the supposed relation between personal outlays, disposable income and interest rates as a mathematical function the economist generates an aura of importance – an aura of being scientific. Most people that are not familiar with mathematical and statistical methods are likely to be reluctant to question the outcome of the analysis of so-called scientific economist.

**Is the mathematical method valid in economics?**

In the natural sciences, the employment of mathematics enables scientists to formulate the essential nature of objects. By means of a mathematical formula, the response of objects to a particular stimulus in a given condition is captured. Consequently, within these given conditions, the same response will be obtained time and again.

The same approach, however, is not valid in economics. For economics is supposed to deal with human beings and not objects.

To pursue quantitative analysis implies the possibility of the assignment of numbers, which can be subjected to all of the operations of arithmetic. To accomplish this, it is necessary to define an objective fixed unit. Such an objective unit, however, does not exist in the realm of human valuations.

On this Mises wrote, “There are, in the field of economics, no constant relations, and consequently no measurement is possible^{[1]}.” There are no constant standards for measuring the minds, the values, and the ideas of men.

People have the freedom of choice to change their minds and pursue actions that are contrary to what was observed in the past.

It is individual goals or ends that set the standard for valuing the facts of reality. For instance, if the goal of an individual is to improve his health, then he would establish which goods will benefit his health and which will not. Among those that will benefit him, some will be more effective than others.

The use of mathematics in economics poses another serious problem. The employment of mathematical functions implies that human actions are set in motion by various factors. For instance, contrary to the mathematical way of thinking, individual outlays on goods are not “caused” by income as such.

In his own context, every individual decides how much of a given amount of income will be used for consumption and how much for savings. While it is true that people respond to changes in their incomes, the response is not automatic, and it cannot be captured by a mathematical formula. An increase in an individual’s income does not automatically imply that his consumption expenditure will follow suit. Every individual assesses the increase in income against the goals he wants to achieve. Thus, he might decide that it is more beneficial for him to raise his savings rather than raise his consumption.

**The validity of probability theory in economics **

Modern economics in addition to sophisticated mathematics also employs probability distributions. What is probability? The probability of an event is the proportion of times the event happens out of a large number of trials.

For instance, the probability of obtaining heads when a coin is tossed is **0.5**. This does not mean that when a coin is tossed 10 times, five heads are always obtained. However, if the experiment is repeated a large number of times then it is likely that **50**% will be obtained. The greater the number of throws, the nearer the approximation is likely to be.

Alternatively, say it has been established that in a particular area, the probability of wooden houses catching fire is **0.01**. This means that on the basis of experience, on average, **1**% of wooden houses will catch fire. This does not mean that this year or the following year the percentage of houses catching fire will be exactly **1**%. The percentage might be **1**% or not each year. However, over time, the average of these percentages will be **1**%.

This information, in turn, can be converted into the cost of fire damage, thereby establishing the case for insuring against the risk of fire. Owners of wooden houses might decide to spread the risk by setting up a fund. Every owner of a wooden house will contribute a certain proportion to the total amount of money that is required in order to cover the damages of those owners whose houses are going to be damaged by the fire.

Note that insurance against fire risk can only take place because we know its probability distribution and because there are enough owners of wooden houses to spread the cost of fire damage among them so that the premium is not going to be excessive.

In his writings, Ludwig Von Mises labelled this type of probability as a class probability. According to Mises,

Class probability means: we know or assume to know, with regard to the problem concerned, everything about the behavior of a whole class of events or phenomena; but about the actual singular events or phenomena we know nothing but that they are elements of this class.

^{[2]}

Thus, the owners of wooden houses are all members of a particular group or class that is going to be affected in a similar way by a fire. We know that, on average, **1**% of the members of this group is going to be affected by fire. However, we do not know exactly who it will be. The important thing for insurance is that the members of a group must be identical as far as a particular event is concerned.

**Why probability distribution not relevant in economics?**

In economics, we do not deal with identical cases. Each observation is unique and not a member of any class – it is a class on its own. Consequently, no probability distribution can be established. (Again, probability distribution rests on the assumption that we are dealing with identical cases).

Let us take for instance entrepreneurial activities. If these activities were identical with known probability distributions, then we would not need entrepreneurs. After all, an entrepreneur is an individual who arranges his activities toward finding out consumers’ future requirements. People’s requirements however, are never constant with respect to a particular good.

Since entrepreneurial activities are not identical, this means that probability distribution for entrepreneurial returns cannot be formed. For instance, in year one, an entrepreneurial activity yielded **10**% return on investment. In year two another entrepreneurial activity produced a return of **15**%. In year three a third entrepreneurial activity secured a return of **1**%, and in year four a fourth entrepreneurial activity generated a return of **2**%. The average of these returns is **7**%.

By no means, however, does it imply that we can establish a probability distribution of returns on the basis as one can establish for the risk of fire, or for obtaining heads in tossing a coin. The returns in various years are the result of specific entrepreneurial activities. These activities are not alike and repeatable and cannot be regarded as members of the same class.

Profit emerges once an entrepreneur discovers that the prices of certain factors are undervalued relative to the potential value of the products that these factors, once employed, could produce. By recognizing the discrepancy and doing something about it, an entrepreneur removes the discrepancy, i.e., eliminates the potential for a further profit.

The recognition of the existence of potential profits means that an entrepreneur had particular knowledge that other people did not have.^{[3]} Mises labelled this as a case probability which he defined as,

Case probability means: We know, with regard to a particular event, some of the factors which determine its outcome; but there are other determining factors about which we know nothing.

^{[4]}

Mises held that case probability is not open to any kind of numerical valuation. Human action, cannot be analyzed in the same way that one would analyze objects where the class probability is relevant.

To make sense of the data in economics one must scrutinize it not by means of statistical methods but by means of trying to grasp and understand how it emerged.

The assumption that mainstream economics makes that probability distribution is a valid concept in economics leads to absurd results. For it describes not a world of human beings who exercise their minds in making choices, but machines.

The employment of probabilities in economic analyses implies that a random process generated the various pieces of economic data in similarity to tossing a coin. Note that random means arbitrary i.e. without method or conscious decision. However, if this had been the case human beings would not be able to survive for too long.

In order to maintain their life and wellbeing, human beings must act consciously and purposefully. They must plan their actions and employ suitable means.

Now if numerical probability cannot be established in economics objectively what about subjective probability? The moment one moves into the subjective assignments of numbers, one could say anything.

One could say that based on personal feelings there is a high likelihood of a recession in a few months’ time. Alternatively, one could say that he feels that the stock market must correct very soon.

This way of stating things is derived from personal experience or some knowledge that an individual has. This is part of case probability, i.e. we know with regard to a particular event certain things, there are however, other determining factors about which we know nothing.

For instance, we know that an increase in money supply is likely to exert in the future an upward pressure on the prices of goods. We however, cannot be certain that prices are going to increase since there could be other offsetting factors about which we know nothing.

**Summary and conclusions**

Contrary to popular thinking, advanced mathematical and statistical methods are not applicable in economics. For instance the use of numerical probability is relevant in the sphere of non- economics where we deal with identical cases. This is however not so in economics. Consequently, no probability distribution can be established in economics as such. Human action cannot be analyzed in the same way that one would analyze objects. Various quantitative methods are a way of describing but not explaining events. These methods do not improve on our knowledge of the driving factors in economics. A major problem of using mathematics in economics is that it distracts economists from thinking about the essence of what causes economic events. To make sense of historical data one must scrutinize it not by means of quantitative methods but by means of trying to grasp and understand how it emerged.

[1] Human Action, p.55.

^{[2]} Ludwig Von Mises, Human Action, Revised Edition, Contemporary Books Inc, Chicago P 107.

^{[3]} Murray N. Rothbard, Man, Economy, and State (Los Angeles: Nash), Vol 2, p 466.

^{[4]} Human Action, p 110.