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In the 'book of why' he says:

the listening pattern prescribed by the paths of the causal model usually results in observable patterns or dependencies in the data

I don't understand, why he says "usually". Isn't it always the case when we have causation that we shall see some sort of dependence in the data?

Then, I really can't follow why he says this:

"There is no path connecting D and L" which translates to a statistical statement "D and L are independent".

Correct me if wrong, but the absence of a path only means there is no causation... Why he says D and L are independent? I mean, both D and L can be highly correlated and still we could see no path connecting D and L.

Both quotes are from page 13.

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    $\begingroup$ For the first part, maybe the case of offsetting/cancelling effects is relevant. It is rarely plausible but not technically impossible. $\endgroup$ Commented Mar 25, 2021 at 16:46
  • $\begingroup$ There's a distinction between path and directed path, where the latter must follow the direction of causality (arrows), and the former does not. And it sounds like you're thinking of "directed path." So $X \leftarrow Z \rightarrow Y$, says $X$ and $Y$ are both are caused by $Z$. $X$ and $Y$ might be correlated, but neither causes the other. There is no directed path between them, but there is a path between them (since they have a shared cause). Does that help? $\endgroup$
    – bogovicj
    Commented Mar 25, 2021 at 20:48
  • $\begingroup$ Also remember that the lack of an arrow between two variables in a DAG means no direct causal effect, not no causal effect. For example, in the DAG $A \to B \to C$, $A$ is for sure a cause of $C$, even though it is not a direct cause of $C$. $\endgroup$
    – Alexis
    Commented Mar 31, 2021 at 18:05

2 Answers 2

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I don't understand, why he says "usually". Isn't it always the case when we have causation that we shall see some sort of dependence in the data?

No, because you can have accidental cancellations. See here for an example: Does statistical independence mean lack of causation?

Correct me if wrong, but the absence of a path only means there is no causation... Why he says D and L are independent?

You are conflating a directed path with paths in general. Paths do not need to be causal. For instance, consider a third variable $Z$. If $Z$ is a common cause, we have the path $D \leftarrow Z \rightarrow L$ and this induces a non causal association between $D$ and $L$. We call such paths ``back-door'' paths. This is a path very much like $D \rightarrow L$ is a path.

So when we say ``absence of paths,'' we mean a complete absence of any connection between the two variables in the DAG, directly or indirectly. If there are no paths from $D$ to $L$, be it direct or indirect paths this indeed implies independence between the two variables.

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    $\begingroup$ +1 Was going to answer with the link you provided if no else had. :D There is a great example of an automobile's speed and the angle of the accelerator pedal that I am trying to remember a source for that would also be a good example (it is pretty similar to the boat example Dimitriy quoted). :) $\endgroup$
    – Alexis
    Commented Mar 31, 2021 at 17:59
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This only addresses your first question, but I wanted to point out that cancellation does not have to be accidental. It can be the outcome of purposeful human behavior. This is a key point to me since that implies cancellation (and sign-flipping of the correlation) is the norm rather than a once-in-a-very-blue-moon event.

This example is taken from Scott Cunningham's Causal Inference: The Mixtape.

enter image description here

But weirdly enough, sometimes there are causal relationships between two things and yet no observable correlation. Now that is definitely strange. How can one thing cause another thing without any discernible correlation between the two things? Consider this example, which is illustrated in Figure 1.1. A sailor is sailing her boat across the lake on a windy day. As the wind blows, she counters by turning the rudder in such a way so as to exactly offset the force of the wind. Back and forth she moves the rudder, yet the boat follows a straight line across the lake. A kindhearted yet naive person with no knowledge of wind or boats might look at this woman and say, “Someone get this sailor a new rudder! Hers is broken!” He thinks this because he cannot see any relationship between the movement of the rudder and the direction of the boat.

But does the fact that he cannot see the relationship mean there isn’t one? Just because there is no observable relationship does not mean there is no causal one. Imagine that instead of perfectly countering the wind by turning the rudder, she had instead flipped a coin—heads she turns the rudder left, tails she turns the rudder right. What do you think this man would have seen if she was sailing her boat according to coin flips? If she randomly moved the rudder on a windy day, then he would see a sailor zigzagging across the lake. Why would he see the relationship if the movement were randomized but not be able to see it otherwise? Because the sailor is endogenously moving the rudder in response to the unobserved wind. And as such, the relationship between the rudder and the boat’s direction is canceled—even though there is a causal relationship between the two.

This sounds like a silly example, but in fact there are more serious versions of it. Consider a central bank reading tea leaves to discern when a recessionary wave is forming. Seeing evidence that a recession is emerging, the bank enters into open-market operations, buying bonds and pumping liquidity into the economy. Insofar as these actions are done optimally, these open-market operations will show no relationship whatsoever with actual output. In fact, in the ideal, banks may engage in aggressive trading in order to stop a recession, and we would be unable to see any evidence that it was working even though it was!

Human beings engaging in optimal behavior are the main reason correlations almost never reveal causal relationships, because rarely are human beings acting randomly. And as we will see, it is the presence of randomness that is crucial for identifying causal effect.

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  • $\begingroup$ Great excerpt! Is there a technical term for this phenomenon? Searching for "cancelation" in this context doesn't seem to bring up much. $\endgroup$
    – Ryan Volpi
    Commented Mar 30, 2021 at 20:14
  • $\begingroup$ Endogeneity is the term used in economics. The standard example is the estimation of supply and demand curves. $\endgroup$
    – dimitriy
    Commented Mar 30, 2021 at 20:16
  • $\begingroup$ +1 Wish I could give you more, 'cause we need more art. :D $\endgroup$
    – Alexis
    Commented Mar 31, 2021 at 17:59

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