Crosspost
Epistemic Status: Entirely ripped from Chapter 3 of “Causal Inference: The Mixtape” by Scott Cunningham which is graciously provided for free here and is generally a very good textbook. I hope that by writing this I provide a slightly shorter and easier to read explanation of the highlight (imo) of this chapter. All mistakes are my own and not the textbook’s.
I. Simple DAG
Today I woke up and decided I wanted to explain backdoor paths in an intuitive way both to improve my own understanding and because I think it's a useful idea for rationalists working with causation (which is everyone all the time?). Also I find it really interesting, especially the second half.
To explain backdoor paths, we are going to use Directed Acyclic Graphs, or DAGs for short. These sound really scary but they are actually just maps of causality.
A simple DAG looks like the one below.
The letters in a DAG represent variables we are studying. In this case, A, B, and C. The lines represent paths of causality in the direction they are pointing. So here, changes in A cause changes in both B and C. An absence of a line represents the fact that there is no causal pathway between two variables. Changing B will not change C or vice versa. Also, the lines don’t run backwards, so changing either B or C exogenously will not change A.
Because we are only explaining backdoor paths this is all you need to know for now. If you want a better explanation of DAGs you can check out the textbook here. Now let’s get started.
II. Two Confounders
Imagine we suspect that changes in A cause changes in B but we want to estimate the exact relationship. We could maybe regress B onto A to find this relationship. We could even do a bunch of functional form specification stuff if we suspect the relationship is nonlinear. Imagine we do this and get a simple coefficient of 0.7. That is, a one unit increase in A leads to a 0.7 unit increase in B. Let’s write that like this.
But now imagine that our