By Dr Frank Shostak
Most economists regard the use of mathematical and statistical methods as the 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. Economists presenting this relation as
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 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, b are established by means of statistical method called the regression analysis.
By means of another mathematical formulation some economists have established that the personal consumer outlays can be depicted as:
C=a*Yd + a1*C(-1) + a2*C(-2) +a3*(Money/CPI)
Where C(-1) stands for consumer outlays lagged by one month, C(-2) consumer outlays lagged by 2 months. Money stands for the stock of money and the CPI stands for the consumer price index a, a1, a2 and a3 are parameters.
So how we then to decide which mathematical formula should we accept as the valid formulation of the real world? For many economists the criteria for the selection of the “right” formula is how well it fits the data. The higher the correlation the better. Unfortunately, a mathematical formulation cannot help us to ascertain the essence that drives consumer outlays.
A mathematical formulation for consumer outlays just describes the observed outlays. It tells us nothing about the causes for these outlays. According to Mises to arrive at explanation we need to trace the change in the data back to previously established and identified phenomena.
Furthermore, 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.” There are no constant standards for measuring the minds, the values, and the ideas of men.
The main characteristic of human beings is that they are rational animals. They use their minds to maintain their lives and well-being. The usage of the mind, however, is not set to follow some kind of automatic procedure, but rather every individual employs his mind in accordance with his own circumstances. This makes it impossible to capture human nature by means of a mathematical formula. People have the freedom of choice to change their minds and pursue actions that are contrary to what was observed in the past. Because of the unique nature of human beings, analyses in economics can only be qualitative.
In addition, the employment of mathematical functions implies that human actions are set in motion by various factors. However, 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 income will be used for consumption and how much for investment. 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 investment rather than raise his consumption.
The relevancy of probability 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 ten 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 is going to 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.
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 homogeneous as far as a particular event is concerned. In economics however, we do not deal with homogeneous cases. Each case is unique not a member of any class – it is a class on its own.
Let us take for instance entrepreneurial activities. If these activities were homogeneous 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 not constant with respect to a particular good.
Since entrepreneurial activities are not homogeneous this means that probability distribution for entrepreneurial returns cannot be formed.
The returns are the result of specific entrepreneurial activities. These activities are not homogeneous 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. Having this unique knowledge means that profits are not the outcome of random events. 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.
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 employment of probability distribution in economics 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 the various pieces of economic data was generated by a random process in similarity of 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 derived from personal experience or some knowledge that an individual has.
We suggest that this is part of the case probability i.e. we know, with regard to a particular event certain things but there are 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. It will not be of great benefit to arbitrary assign numerical probabilities here.
Summary and conclusions
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 causes 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.