Causality

I read (most of) The Book of Why by Judea Pearl. I read the first four chapters carefully, but less so the remaining of the book, after I thought I understood its main arguments and conclusions. I may come back, particularly if I think I missed key aspects of it, but I will summarize here my current understanding and impressions.

For most of my reading I was somewhat put off by the constant claim of how revolutionary and new the content of the book was, when much of it seemed to simply reflect standard scientific methodology. At first I thought that the claim to a revolutionary new science (“Causal Inference”) perhaps reflected Pearl’s own trajectory, stemming from a computer science background and dialoguing routinely with statisticians, and that perhaps he did not have a strong science background. But that is not the case: I understand he has actually made contributions to physics.

Where I finally saw a rupture with traditional academic practice was when I got to chapter 4 and his discussion of the back-door criterion for selection of variables to control for when assessing models applied to observational data. Social scientists (to exemplify with the academic practice I am most familiar with), when trying to measure the potential impact of a variable X on Y, will typically “control for” any other variable that may also be impacting Y under the argument that this will isolate the effect of X and, therefore, avoid capturing a “spurious” correlation between X and Y, given that we are dealing with observational data and not a controlled experiment (at least in the typical case). Here is where Pearl’s contribution of insisting that modelers design the causal diagram (the theoretical framework) they have in mind, and do not control for variables that actually capture an indirect effect of X, became embarrassingly clear to me. I say embarrassingly both because I am probably guilty of controlling for variables I shouldn’t have in the past and because I realize that what he is saying should be somewhat obvious…and yet that has not always been the case.

If I can summarize his main arguments, they seem to be that:

First, P(Y|X)P(Y|do(X)), in other words, if P(Y|do(X)) reflects the isolated causal effect of X on Y, that we would observe in a controlled experiment (like in a randomized control trial), the P(Y|X) that we capture in observational data is something completely different for at least two reasons: a) it captures the effects of other confounding variables; b) it actually tells us, in itself, nothing about causality. It is the old “correlation does not mean causality argument.” Up to this point, his argument seems to me nothing new. He claims, however, that the language is important to allow us to talk about causality: that the “do(X)” needs to be introduced in our lexicon. Fine.

Second, causal diagrams are key for our proper modeling of causal relationships to be tested by observed data. Consider the model below (Figure 1, not in the book, I made this up). Assume the average success of, say, high school basketball players in dunking the ball, is modeled as a function of the average jumping height of each player, and that this jumping height, in turn, is a function of the average player height and, say, the frequency and intensity of jumping practice on the team. A typical econometric test for the effect of jumping practice on the average dunking success of the players might control for player height to isolate the effect of jumping practice. Pearl’s argument would be that there is no need to control for player height and the way to see this is that, not controlling simulates the situation we would have in an RCT, where any other factors are assumed away because, on average, they should be the same among the treatment and control populations, assuming these are large enough. That said, in this case my understanding is that, if we do control for player height, no harm would be done and the result should be the same, assuming the model is correct.