Thread by @NoahHaber

Do DAGs make it harder to understand regression discontinuity?

Hang with me, the reasoning here is a little complicated (but maybe important). Brief thread.

RDD is conceptually simple. Take an arbitrary threshold-based rule that influences whether decision A or B is made (and nothing else important happens around / due to that line).

People immediately on either side of the line are effectively "randomized" to A or B.

Obvi I am glossing over some important details, but the general idea is pretty straightforward when written out in text, easier with a chart of the decision-rule variable.

It's an instrumental variable, and a straightforward one, right?

Ok, now try to do that with a DAG.

First thought: what about the standard IV DAG?

Z -> A -> Y. Nice and simple.

Except what is Z? And what is the data?

If the decision rule were on test scores, you would probably say Z is "test scores," and then you'd be confused.

The IV isn't test scores; it's an epsilon perturbation around test scores at a specific threshold.

How many DAGs have you seen which have that mouthful written out?

And what happens when you DON'T write it out?

If you don't write it out, it looks like there should be a causal association from test scores to Y (let's say cancer), whatever it is, because test scores are connected to basically everything somehow.

But there isn't, because it's an epsilon perturbation.

You might even be tempted to think that it's a mediation or control-based method, when it is, in fact, an instrument.

An alternative route is to try to take care of that with some complicated selection noding, but that goes way down the path of "so complicated it's useless"

So, the argument goes, if you think about causality primarily through DAGs, you might have a harder time understanding how RDD works, or that it works at all.

But who knows. Thoughts?