Why correlation does not imply causation and what the purpose of quickly measurable indicators is, as told by the gnomes of South Park and the underwear index. February 2017 report.
The South Park Gnomes
It was another day, we were channel surfing, when we stumbled upon an episode of the animated series South Park. On previous lazy days, we'd already found some economic theories mixed into the jokes—especially the seemingly nonsensical ones. So we decided to put on our economist hats and explain to our housemates that we were now working. Then we watched the episode that was just starting, titled "Gnomes," in detail.
For those who didn't have the chance to see it, or if you'd like to watch it again, you can find the episode at the following link . Alternatively, you can access a summary of the episode here: link
The program reminded us of some publications on economics and finance websites that, in a style similar to this section, used that chapter as an example to refer to certain discussions of economic policy, and also to the behavior of micro-entrepreneurs. However, in this article we will use it to explain correlations.
In the episode in question, the four main characters of the series are forced to write an essay on current events. They must do so with Tweek, a strange and nervous boy. However, this boy suggests they write about the mysterious gnomes who keep stealing their underwear.
In the series, it is shown that the reason for this theft is to generate economic benefits, as one of the gnomes says “stealing underwear, big business.”
These dwarfs in a friendly manner reveal to the 4 children the business plan behind the operation, which consists of 3 phases:
- 1 phase: steal underwear
- 2 phase: ?
- 3 phase: Earnings
This is precisely the point we wanted to make. The joke, which can be interpreted in several ways, serves as a starting point for us to explain the measurements and correlations.
Underpants as index
The sale of men's underwear is in fact a well-known indicator of the economic cycle, which is even consulted by economists of the stature of Alan Greenspan, former chairman of the US Federal Reserve (see Men's Underwear Index on Wikipedia).
What is this about? Although it is a product whose sales remain relatively stable most of the time, when a major economic crisis occurs they suffer a very sharp drop: hence the importance of this indicator.
The above means that when one does not have income, one decides to adjust what cannot be seen, so to speak. In the same way, when a recovery begins, sales of underpants grow.
This indicator has the advantage of being very simple to construct. Therefore, data for the Underwear Index is usually available much sooner than the main economic variables, which require more extensive analysis (not to mention GDP).
This advantage is what truly gives the indicator its importance. Measurements of other variables will arrive several months after the recovery has begun. Some will even start to rebound a few months later. Underwear sales react and are measured quickly. We could say they measure the economy minute by minute.
Underpants for cement
In Argentina, several economists have stated in recent days that there are some signs of economic recovery. Indicators such as cement shipments and sales of certain goods show improvement. But the reality is that this supposed recovery (or at least, a slowdown in the decline) is very difficult to confirm. In fact, the latest available activity data continue to show year-on-year declines.
The difficulty lies precisely in the lack of real-time economic data necessary to conduct such an assessment. For example, in the case of industrial activity, as of the date of this report, the latest available measurement of the Monthly Industrial Estimator dates from the end of January.
So if, in a hypothetical situation, a recovery occurs from February onwards, we will have to wait until the end of March to be able to observe it.
This highlights the importance of having various indicators that can be quickly calculated and analyzed to draw preliminary conclusions. And this is important not only for the public sector, but also for the private sector.
Imagine a private investor who manages to anticipate an economic recovery. They could, therefore, make decisions in advance and gain an advantage over their competitors—the example becomes extreme in the stock market. The underwear index provides very partial information, that's not up for debate, but it has the advantage of immediacy.
The gnomes' mistake
Now, although the color data may be interesting, it is not the only topic that was sought to be discussed in this article. Let's go back to the episode of the animated series again: why do gnomes steal underwear? Apparently, because they interpreted the data incorrectly.
Imagine one of the gnomes behind a monitor observing the data on the performance of the American economy. What would he observe? That every time underwear sales increase, the economy is on the verge of recovery.
Or, conversely—even more clearly—just before sales of everything else start to fall (which will then lead to a reduction in production), underwear sales fall. Thus, they assume that more underwear leads to better economic performance, simply because there is a correlation between the two variables.
Causality?
This is the point we wanted to make. The problem is that the gnomes can't distinguish between a simple correlation between two variables and a causal relationship between them. Two series or indicators are correlated when they vary similarly (or negatively correlated if they vary inversely).
But from no point of view does that imply that one is necessarily the cause of the other. This distinction is fundamental, and can lead to many misinterpretations. The thing is that we encounter these types of statements every day.
In fact, many times ordinary people or even professional journalists assume that any correlated series can be presented as evidence of some kind of argument they defend.
In view of taking the argument to absurdity, it must be taken into account that some correlated series do not make the slightest sense.
Meaningless correlations
For example , the following graph shows a very tight correlation between the number of people who drowned by falling into a swimming pool in the US versus the number of Nicolas Cage's appearances in movies per year (for more examples of spurious correlations, you can visit the following link: http://www.tylervigen.com/spurious-correlations ).
Note also that the correlation between two variables refers to the degree of variability associated with each one, rather than the level that each one reaches in the measurement.
Even more importantly, when there are two correlated series, in many cases it is difficult to establish which variable generates the other, that is, which one causes which one.
For example , if we examine data on crimes committed and police officers assigned to each neighborhood, we might see that more crimes are committed where more police officers are assigned. Can this be taken as evidence against the effectiveness of the police? Surely not. On the contrary, the government is more likely to decide to send more police officers to areas where more crimes are committed.
From sunspots to chocolate
In this regard, one of the best-known anecdotes in the history of economic thought is the peculiar theory of William Stanley Jevons (1835 – 1882), who argued that economic crises do not occur by chance but by causality.
In his book " Trade Crises and Sunspots ", Jevons presented statistical data relating sunspots to economic cycles, under the hypothesis that sunspots affect the climate, and therefore the harvests.
Recently, a news report cited a study that suggested thin people tend to consume more chocolate than overweight people. Don't get too excited, though; it's probably not that chocolate helps you lose weight, but rather that those who are already obese try to avoid it.
In short, we have several options. It could be that variable A causes B, or that variable B causes A, or even that there is a variable C that could be an intermediate variable or the cause of both A and B. Finally, we also have chance (which is often very difficult to rule out).
When conducting serious economic research to estimate the effects of a particular policy measure, we are faced with a problem of causal inference . That is, we want to evaluate the program's effect on outcomes. It is therefore essential to try to isolate the effects in order to establish the extent to which that program alone has contributed to changing an outcome.
There are several techniques, but the fundamental point is that, if you want to test, for example, whether the police reduce crime, you must analyze an allocation of police officers that is not correlated with crime levels, because otherwise you would arrive at a highly biased result.
Money and inflation: what causes what?
Another example in economics, frequently used by the media, relates to the most common explanations for inflation . Generally, one of these explanations states that inflation is caused by changes in the money supply.
They argue that increasing the money supply raises the price level. Moreover, some economics textbooks actually begin by showing a strong correlation between the money supply and the inflation rate. But is this irrefutable evidence? Not necessarily. Remember this mantra:
“Correlation does not imply causation”
Other theories, known as endogenous money theories , actually argue that inflation is what generates an increase in the money supply. This is because it influences the nominal amount of loans granted by banks [1].
From this delirious episode of the animated series, we can extract, in short, two very important lessons for economic analysis. First, indicators that can be measured quickly are valuable. Second, the fact that two series show similar behavior does not imply that they are causally related.
Of course, the fact that this other theory is true does not invalidate the fact that the first one can be true as well. And in particular, the theory of endogenous money loses validity when the increase in the money supply is derived from a greater monetary base and not from a greater multiplier.
Open access, for use and citation
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- 🗄️ UNR Hypermedia Repository (RepHip): https://hdl.handle.net/2133/17522
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Gnomos, calzoncillos y… correlación. Informes del Observatorio UNR N.º 36 — Serie Puente Académico N.º 12, febrero de 2017. ISSN 2683-9067 / 2683-9091. Autores: Germán A. Tessmer y Luciano A. Jara Musuruana.