Chapter 4, mediator graph and explanation

[AbeKeijts]

Dear Matheus,

I have a question about chapter 4, the last example (the mediator one), where you say conditioning on white collar biases the estimated effect of education on earnings. I think your explanation below the graph assumes another source of bias than the picture suggests. Specifically, your explanation makes it seem that white collar is actually a collider to education and motivation, and conditioning on it opens up a path from education to motivation, and from motivation to wage (this bias would also arise if white collar had no direct impact on wage, right?!). It seems to me that your explanation does not match the graph. I think, when we assume your graph to be the truth (so without motivation), the bias arises because white collar is a non-collider (between educ and wage), and conditioning on it blocks a path from educ to wage. However, I struggle to come up with an explanation based on the potential outcomes notation. In fact, I wonder if there is a way to describe it in that sense. Isn't this just a matter of changing the question from full causal impact of education, to only direct effect? Hence, aren't we just changing the meaning of T as we condition on white collar, and hence will end up to an answer to a different question than we initially intended?

I hope you can help me clarify this, as I keep thinking it over but don't manage to fully wrap my head around it.

Btw, I appreciate your book and posting it online for free, it's very helpful!

Kind regards,
Abe