Lecture 15 Drawing Causal Diagrams

Nick Huntington-Klein

Last time we covered the concept of “controlling” or “adjusting” for a variable
And we knew what to control for because of our causal diagram
A causal diagram is your model of what you think the data-generating process is
Which you can use to figure out how to identify particular arrows of interest

Today we’re going to be working through the process of how to make causal diagrams
This will require us to understand what is going on in the real world
(especially since we won’t know the right answer, like when we simulate our own data!)
And then represent our understanding in the diagram

Consider all the variables that are likely to be important in the data generating process (this includes variables you can’t observe)
For simplicity, combine them together or prune the ones least likely to be important
Consider which variables are likely to affect which other variables and draw arrows from one to the other
(Bonus: Test some implications of the model to see if you have the right one)

Drawing an arrow requires a direction. You’re making a statement!
Omitting an arrow is a statement too - you’re saying neither causes the other (directly)
If two variables are correlated but neither causes the other, that means they’re both caused by some other (perhaps unobserved) variable that causes both - add it!
There shouldn’t be any cycles - You shouldn’t be able to follow the arrows in one direction and end up where you started
- If there should be a feedback loop, like “rich get richer”, distinguish between the same variable at different points in time to avoid it

Let’s start with an econometrics classic: what is the causal effect of an additional year of education on earnings?
That is, if we reached in and made someone get one more year of education than they already did, how much more money would they earn?

We can start with our two main variables of interest:
- Education [we call this the “treatment” or “exposure” variable]
- Earnings [the “outcome”]

Then, we can add other variables likely to be relevant
Focus on variables that are likely to cause or be caused by treatment
ESPECIALLY if they’re related both to the treatment and the outcome
They don’t have to be things you can actually observe/measure
Variables that affect the outcome but aren’t related to anything else aren’t really important (you’ll see why next week)

There’s a lot going on - in any social science system, there are THOUSANDS of things that could plausibly be in your diagram
So we simplify. We ignore things that are likely to be only of trivial importance [so Phys. ed is out!]
And we might try to combine variables that are very similar or might overlap in what we measure [Socioeconomic status, Demographics, Location -> Background]
Now: Education, Earnings, Background, Year of birth, Location, Compulsory schooling, and Job Connections

Consider which variables are likely to cause which others
And, importantly, which arrows you can leave out
The arrows you leave out are important to think about - you sure there’s no effect? - and prized! You need those NON-arrows to be able to causally identify anything.

Remaining: Background, Year of birth, Location, Compulsory schooling, and Job Connections
All of these but Job Connections should cause Ed