Economists Do It With Models

Correlation Does Not Imply Causation, Reverse Causality Edition…

December 18th, 2011 · 36 CommentsUncategorized

Since you seemed to like the correlation charts from yesterday, I figured I would give you one more related item.

When two events A and B are correlated (i.e. happen together), we can’t tell whether event A caused event B (rain caused me to bring my umbrella), event B caused event A (bringing my umbrella caused it to rain), or some event C caused both event A and event B (the existence of storm clouds caused both the rain and the umbrella-bringing). We point out a lot of situations where the real explanation is the think with the outside C event and relatively few with the “reverse causality” explanation, probably because a lot of the reverse causality scenarios don’t pass the sniff test of sanity. (I don’t like assuing things based on intuition, but even I would feel comfortable ruling out the possibility that bringing my umbrella caused it to rain.) Nonetheless, reverse causality is entirely possible, and even sort of has its own name:

Technically, these cases show both forward and reverse causality, resulting in various forms of unfortunate cycles. True reverse causality would be like that time in high school where my boyfriend’s parents told me I could eat whatever I wanted because I was skinny. Luckily for them (or not, in a way), I didn’t get on my correlation versus causation soapbox until years later.

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36 responses so far ↓

• 1 Chris // Dec 18, 2011 at 3:04 pm

Post hoc ergo propter hoc!

• 2 idahotradeguy // Dec 18, 2011 at 3:04 pm

I am grading economics essay finals right now. Instead of explaining to my students the error of their argument, I can now point them to this blog post.

Thanks EconGirl!

• 3 John Fitzgerald // Dec 18, 2011 at 5:07 pm

I checked the mathematics with a brilliant mathematician. Somewhere, I have the proof. What mathematical correlation proves is mathematical equivalence, |u|/u=|v|/v. Correlation presents no other information.

Causality is an entirely separate issue that comes out of the relationship between the two dynamic factors being measured and the relationship between the measure and the factor.

There are physical processes that have specific forms. The rate of flow of water exiting an orifice at the bottom of a column of water follows an exponential decay. The rate of decay of radiation is identical in it’s form. Measured and compared, the two are perfectly correlated. But, they have no physical connection. There is no causality.

Even when related, the perception of causality is over rated. We, as human beings, have a subjective bias to need causality. I need to know that I can affect my world and, as such, need to know what I can cause.

But, even in simple systems, two dynamic quantities simply exist together. They are inextricably link. Interrupting the system, in any manner, whether by affecting a change to factor A, factor B, or some other factor, causes the system to change and both correlated measure change simultaneously.

Interestingly, a lack of mathematical correlation, doesn’t prove a lack of equivalence. This has to do with how the two measured factors are being lined up.

My familiarity with electronics provides for a simple example, the relationship between current and voltage in an AC system. Typically, these lead or lag each other by 90 degrees. And, when matched in an examination of correlation, they are uncorrelated.

The mathematical meaning of correlation, that |u|/u=|v|/v, is absolutely sound when we adhere to it’s meaning absolutely. It tells us simply that the two quantities are mathematically identical. To be clear, they are mathematically indistinguishable. They are the same thing.

To be clear, the result of |u|/u|v|/v simply tells us nothing. Any further proof of this must come from a further examination of the connection physics of the systems being examined.

So, correlation means, mathematically identical. A lack of correlation means nothing.

Mathematical correlation is absolutely remarkable in what it proves. And yet, in isolation, it means absolutely nothing.

• 4 John Fitzgerald // Dec 18, 2011 at 8:08 pm

I should explain what the mathematical formula, |u|/u=|v|/v, means in words. My computer suffered some problems the other day and now just beeps incessantly. My notes on the fundamentals of numerical methods and correlation are no longer available to me.

It may be better written as u/|u|=v/|v|, or u/avg(u)=v/avg(v). There are more complicated definitions involving calculus. All of them just express the same thing. They are just shorthand for a simple idea that is best expressed in words.

It means that the two quantities differ only in magnitude or scale. The simplest would be the correlation between something measured in feet and in inches. These measurements are, obviously, absolutely correlated. They differ only in magnitude or scale.

This example of a measurement in inches and in feet, being mathematically correlated, presents the very nature of correlation in it’s entirety.

We wouldn’t say that the measurement of feet causes the measurement of inches, or the other way around. The time, as expressed on a clock, is correlated to the movement of the sun. Mathematical correlation will show them to be identical, with an adjustment of scale. But, we wouldn’t say that one causes the other.

This correlation between the sun and a clock give us an a simple example with which to consider what causality means. We recognize that there is a complex connection of causality that drives them both. There is a real relationship of tertiary causality because, through the incredibly complex nature of the biology of human beings, one was designed to be correlated with the other. The clock was set in motion to be correlated with the sun, even though, beyond that point there is no instantaneous physical connection between the two.

Another example would be a stick in the ground which, when it’s shadow is measured, is correlated with the position of the sun. Mathematically, a measure of the sun’s position and the shadow’s position are the same thing. They are identical with the only difference being that of scale of the units of measure. The direction of causality is obvious to anyone. It would be an interesting effort to prove this.

• 5 bdbd // Dec 18, 2011 at 9:22 pm

How about “No one is going to understand them anyway, so economists do it with models?”

• 6 Jake Lopata // Dec 19, 2011 at 2:56 pm

If you don’t understand the nature of correlation, then how can you understand the graph/models?

Correlation helps to create underlying ASSUMPTIONS for your models, of which need to follow some reasonable logic.

• 7 Joseph // Dec 21, 2011 at 6:49 pm

We see reverse causality in epidemiology all of the time when working with pharmaceutical drugs. People take drugs to combat early disease symptoms. The drugs are then associated with the outcome of interest. However, it was the disease process that caused the drug use, not the drug use that caused the disease.

Tricky stuff.

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