Correlation ≠ Causation
Often we observe that two pieces of data, which are not supposed to have any relationship, appear to have very high visual correlation. For instance, we may discover strong correlation between the intensity of a dog barking and movements in stock prices. One is then tempted to take advantage of this discovery in order to make money in the stock market.
In reality however, both the barking of the dog and the movements of the stock indexes have nothing to do with each other. What may make the apparent good correlation is that they both exhibit an upward long-term trend. In addition, fluctuations of these data do not seem to converge around the trend but just seem to move in an upward direction. These types of data statisticians label non-stationary.
In contrast, data that converges around a fixed value is labeled stationary. Data that is stationary implies an unchanged structure, something that is stable and hence one can make sense of it, whereas non-stationary data is associated with irregular fluctuations, which of course makes it very difficult to make any sense of. Thus if something drifts aimlessly it is not possible to say much about its future course. If one tries to make sense out of the data that is irregular, obviously one will not get very far. This, however, creates a major problem for economists if the data that economists and financial analysts are employing are not stationary. Consequently, incorporating these types of data into economic analyses leads to misleading results.
For instance, an economist wants to establish the importance of changes in production on peoples’ consumption. The common procedure for this is to apply statistical methods on consumption and production data in order to establish their interrelationship.
By means of a statistical technique, also known as regression analysis, one establishes how consumption and production are quantitatively connected to each other.
Let us assume that an economist has found that the relationship between consumption and production is summarized by the following mathematical expression:
Consumption = 10 +0.5*Production
Armed with this finding the economist can now tell us the direction of consumption if there is a change in production. Thus if production is 100 then consumption will be 60 (because 10+0.5*100=60). Economists label the numbers 10 and 0.5 as parameters.
Observe that the information regarding the size of these parameters (i.e. whether they are 10 and 0.5 or something else) is obtained by means of the regression technique. The numbers 10 and 0.5, which were generated by regression method, are the estimates of true parameters in the real world, or so it is held.
It is maintained that on average these estimates are very close to the true parameters. It is also believed that any conclusions derived from the equation regarding the relationship between consumption and production is a reflection of reality, as long as the model performance in terms of its forecasting capability is good.
The Nobel Laureate Clive Granger, however, contests this.1 He argues that no meaningful conclusions can be drawn from the above equation if the data employed in establishing this equation is non-stationary. In fact, according to Granger the data that economists were employing in the past research was likely of non-stationary nature.
The parameters that one obtains from such data are likely to be misleading and hence the outcome of the analysis is likely to be meaningless. So how does one overcome the problem?
If one were to establish a common factor that influences both consumption and production then these two time-series are said to be connected, or co-integrated. Granger and others have shown by means of mathematical and statistical methods that the introduction of a common factor makes the interrelationship between non-stationary time series stationary.
Thus, consumption and production can be observed separately as a non-stationary time series. If one were attempting to establish economic relationships between them, one will get misleading results. However, if one were to establish that both consumption and production have a common factor then one could infer that over time both consumption and production must move together.
This common or co-integrating factor could be that people's wellbeing requires consumption and production. Moreover, that without production there cannot be consumption and without consumption, no production is possible.
Another example is an identical good, which is trading in different locations. The day to day fluctuations in prices may appear to be random in various locations and therefore most likely will not correspond to each other.
However, the existence of arbitrage and the law of supply and demand will make sure that over time prices in various locations will move close to each other.
Instead of trying to find out what the co-integrating factor is, Granger and others have produced a mechanized framework, which enables economists to establish whether the data complies with co-integration i.e. whether the relationship between the data makes sense so to speak. Once it is established that the data is co-integrated it can then be employed by a certain mathematical procedure to establish the correct parameters.2
Various statistical results that are produced by means of the Granger’s framework therefore are regarded as valid since they have been applied on co-integrated data.
Granger’s method raises serious doubts about past conclusions regarding economic interrelationships, which were reached by means of the old techniques. It also provides a criticism of the popular usage of correlations without attempting to make sense of the relationships.
Granger's framework seems to provide economists with a powerful tool that helps to minimize the use of meaningless correlations. For instance, the Granger framework will indicate that movements in the stock market and the intensity of the dog barking cannot be co-integrated and therefore the use of these relationships to make money in the stock market could prove to be a very expensive exercise.
In this respect, it could be regarded as bringing back the validity of fundamental analysis. This must be contrasted with the popular way of thinking that fundamental analysis is of little help because as a rule the data is of a random nature. Therefore, it seems that the Granger's framework is a great tool in furthering our understanding of the economic universe. However, is it?
Are there Constants in Economics?
The major issue that Granger has not addressed is not whether the old techniques have been generating valid parameters estimates, but whether such parameters exist at all.
In the natural sciences, the employment of mathematics enables scientists to formulate the essential nature of objects. Consequently, within given conditions, the same response will be obtained repeatedly. The same approach, however, is not valid in economics. For economics is supposed to deal with human beings and not objects. According to Mises,
The experience with which the sciences of human action have to deal is always an experience of complex phenomena. No laboratory experiments can be performed with regard to human action.3
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. There are no parameters in the human universe. Thus Mises wrote,
There are, in the field of economics, no constant relations, and consequently no measurement is possible.4
The popular view that human economic activity can be captured by a mathematical formulae expressed through fixed parameters implies that human beings are operating like machines. 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 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. For instance, 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.
At best, mathematical formulations can be seen as a technique to provide a snap shot at a given point in time of various economic data. In this sense, it can be seen as a particular form of presenting historical data. These type of presentations, however, can tell us nothing about the driving causes of human economic activity. What's more, the employment of established historical relations to assess the impact of changes in government policies will produce misleading results notwithstanding Granger’s framework.
After all, to assume that a change in government policy will leave the structure of the equations intact would mean that individuals in the economy ceased to be alive and were, in fact, frozen.
In this regard Mises wrote,
As a method of economic analysis econometrics is a childish play with figures that does not contribute anything to the elucidation of the problems of economic reality.5
We suggest that causality cannot be ascertained by means of mathematical methods but by means of understanding. This in turn can be done once the framework of our thinking is based on a non-refutable axiom such as human beings use means to attain ends. With the help of this approach, one is going to establish that causality emanates from humans themselves and not outside factors.
There are no constant standards for measuring the minds, values, and ideas of men. Valuation is the means by which a conscious purposeful individual assesses the given facts of reality. An individual establishes what the facts are, he then assesses which out of these established facts are the most suitable to attain his various ends.
Individual goals or ends 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. There is no way, however, to quantify the effectiveness. All that one could do is rank these goods in accordance with perceived effectiveness.
- 1. Granger, C.W.J. and Newbold, P. (1974) "Spurious Regressions in Econometrics", Journal of Econometrics, Vol. 2, pp 111-20.
- 2. Granger, C.W.J. and Weiss, A. A. 1983, "Time series analysis of error-correction models," in S.Karlin, T. Amemiya and L.A. Goodman, Studies in Econometrics, Time series and Multivariate Statistics, in Honor of T.W. Anderson, Academic Press, San Diego, pp 255-278.
- 3. Ludwig von Mises, Human Action (1963), p 31.
- 4. Human Action, p 55.
- 5. Ludwig von Mises, The Ultimate Foundation of Economic Science (1962), p 63.