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Reader Question: But Does Causation Imply Correlation?

November 6th, 2009 · 15 Comments
Reader Questions

I write a lot on the danger of believing the “post hoc ergo propter hoc” fallacy (which is basically a fancy Latin way of saying “One thing happened after another thing, therefore one thing happened because of another thing), also known as “don’t be stupid people, correlation does not imply causation.” To recap:

A Primer On Correlation Versus Causation, This Time With Stick Figures…
On Why The New York Yankees Aren’t Like Groundhogs…
On “The Least Surprising Correlation Of All Time”, SAT Scores Edition…
First Comes Love, Then Comes Obesity…
Truth In Advertising, Home Cooked Meals Edition…

Apparently I’m not the only one who likes the stick figure example, since it’s now being made into a t-shirt:

(I have to admit that I only just now got the full extent of the joke after seeing the cartoon like 500 times.)

I can’t tell if my friend was trying to be cute or genuinely inquisitive (or both) by posing the following question in response to my post on the relationship between Yankee success and economic health: “Yes, but does causation imply correlation?”

Apparently this is what it’s like to have really smart friends- I rarely know when they are kidding. So I gave an actual response:

“Dude, you just blew miy mind with that. Um…I was at first going to flippantly say that it did, but I think I can come up with counterexamples. Think about a case where a number of different things could cause a particular event. (an appropriate example event is “me going to Dunkin Donuts for iced coffee) Because there are so many causes, any… Read More one of which would trigger the DD run, the DD run usually happens. Therefore, even though something like “need to walk the dog” causes the DD run, the correlation wouldn’t have to be very high since I go to DD most of the time regardless of whether I have to walk the dog. (In other words, even though knowing that I walked the dog tells you that I went to DD, knowing that I went to DD gives you very little information about whether I walked the dog.) Does that sound right?”

So now you know, in case you too had that nagging question in the back of your mind.

(In case you were wondering, correlation generally just refers to two things moving together, either in the same or in opposite directions. You can read more about the specifics of correlation here. An easy way to remember the difference is that correlation is symmetric whereas causation is not- If A is correlated with B, then by definition B is correlated with A. It is certainly not true that if A causes B then B causes A.)

Tags: Reader Questions

15 responses so far ↓

  • 1 dWj // Nov 6, 2009 at 3:33 pm

    Two people pick random numbers between 0 and 1; the numbers are added and, if they exceed 1, 1 is subtracted. Conditional on what either party knows, the final number is uniformly distributed between 0 and 1. I would say that each causes the result, yet neither correlates with it.

  • 2 Julia // Nov 6, 2009 at 3:40 pm

    I’m going to argue with the dog / coffee theory and say that they’re correlated, not causal. You don’t get coffee BECAUSE you’re walking the dog, you get coffee while walking the dog because you like coffee (as evidenced by your getting coffee at other times too).

    I could argue (I’m not sure how convincingly) that causation may lead to correlation of different things depending on external factors. Using the hot weather, ice cream and air conditioner sales old saw, in a bad economy hot weather might more likely drive up cheaper cooling options (public pool attendance) while in a flush economy it might drive up more expensive cooling options (individual air conditioner sales). Hot weather has a causal relationship with cooling activities, but it might be hard to predict which ones.

  • 3 econgirl // Nov 6, 2009 at 5:19 pm

    Oh, the dog walking is causal in the situations where nothing else is prompting me to get the coffee. (I set up the scenario very carefully as such.) The way you can check is to consider the counterfactual: if the world was exactly the same save for my dog being asleep rather than scratching at the door, would I have still gotten the coffee? If the answer is no, then I can conclude that the dog walking caused me to get the coffee. Notice, however, that the causal impact is only directly (read, on the margin) present when nothing else is causing me to get the coffee.

  • 4 josh frank // Nov 6, 2009 at 7:53 pm

    Things become much murkier when you consider that causation is psychologically and socially constructed (not that things don’t cause other things to happen, but that there are countless levels of causation). With the dog/coffee case you can talk about the dog, or the mental states or the social forces or neurons or molecules or atoms, or the specieist/patriarchial/whatever structure of society etc. and all are true from a certain perspective.
    And this becomes really problematic for science (especially an imprecise science like economics) because we scientists go right to the link being causation when we are inclined to believe the underlying theory, but then we invoke correlation does not imply causation when it would cause us cognitive dissonance/challenge our beliefs. As a result, inaccurate beliefs and paradigms within a field linger on and die slowly and painfully.

  • 5 holmegm // Nov 7, 2009 at 12:11 pm

    also known as “don’t be stupid people, correlation does not imply causation.”

    Which line always bugs the @#$ out of me.
    Of course correlation implies causation … it just doesn’t guarantee causation.

  • 6 Tony // Nov 8, 2009 at 5:52 pm

    Without knowing your motives for dog walking/coffee drinking, I would imagine that the urge for coffee sometimes causes you to walk your dog.

    That’s what I thought you meant by the dog walking story. Here’s how this would go.

    Suppose you have a hankering for a cup of Dunkin’. When you have this urge, you may turn to your pup and say “Hey, want to go for a walk?” If walking often results in treats (dogs respond to incentives, too), much tail wagging would ensue. The dog agrees happily to a walk, and you get your coffee. They correlate, but in this story, it’s because you want an excuse to get some coffee. Why waste a perfectly good walk? And, in this case, no urge for coffee ==> no dog walk.

    Then again, that’s just a story. In this case only econgirl knows what causes what.

  • 7 Ben // Nov 9, 2009 at 2:44 pm

    I don’t think I buy your example; the statement isn’t, “causation implies perfect correlation”; your dog-walking coffee causation does add correlation to dog-walking and coffee, even if coffee isn’t majority-caused by dog-walking. If you decided to only get coffee while walking the dog if a coin turned up heads, wouldn’t R^2 between dog-walking and coffee be less than it is now? What is the threshold for correlation to be implied?

  • 8 Lucas M. Engelhardt // Nov 12, 2009 at 10:41 pm

    holmegm,

    You’re confusing two definitions of “implies”.

    Defn 1: “common speak” – “implies means ‘suggests'”. In this sense, yes, correlation implies causation.

    Defn 2: “logic speak” – “implies means ‘involves by logical necessity'”. When I say “A implies B” (in the logical sense), then that means “If A is true, then B is also definitely true.” In this sense, correlation does not imply causation. Because correlations can happen where there is no causal link.

    When speaking in terms of logical fallacies, it’s sensible to believe that the “logical” definition is the one being used.

    On the OP,

    I think the trick here is that in reality there are multiple causes for observed phenomena. So, one causal link may get overwhelmed by other causal links. But, I’m reasonably confident that causation does imply conditional correlation… Causal links are “ceteris paribus” – and with conditional correlations we hold the “ceteris” “paribus”.

  • 9 Shannon // Dec 31, 2009 at 1:00 pm

    I would argue that in the dog walking/DD run example the causation does imply correlation, because there is a predictive relationship between dog walking and coffee buying, and thus a correlation. There may be other causes of coffee buying that have a stronger correlation than dog-walking, but that doesn’t mean the dog walking correlation does not exist, only that it is comparatively weak.

    The only instance I can think of where cause and effect would not be correlated is if you have multiple causes that are necessary for a given effect, but which are not by themselves sufficient to cause the effect. For example, my two causes could be dog walking and availability of spending money. I will only buy coffee if both causes come in to play, so there will not be much of a correlation between dog walking and coffee purchasing if my model doesn’t take in to account whether I have any spending money. Of course you could then argue that my model is faulty and I should be putting a bit more effort into my research, but that’s a different story entirely.

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