Meeting Dates

Monday, October 24, 2022

## Overview

Today we return to a more nuanced discussion of causality, given what we have learned about the fundamental problem of causal inference (counterfactuals and potential outcomes). RCTs are great, but they are not everything — and in any case, you are never going to be able to design and run an RCT in the overwhelming majority of studies.

Now that we understand counterfactuals, we can apply our idea of exogeneity to argue that indeed, yes, correlation does imply causation when $$X$$ is exogenous! That is, $$X$$ being correlated with $$Y$$ implies there is a causal connection between $$X$$ and $$Y$$, and if we are certain that $$cor(X,u)=0$$, then we are clearly measuring the causal effect of $$X \rightarrow Y$$! If $$cor(X,u) \neq 0$$ and $$X$$ is endogenous, there is still a causal connection between $$X$$ and $$Y$$, but it goes through other variables that jointly cause $$X$$ and $$Y$$.

We also introduce a new tool for thinking about simple causal models, the directed acyclic graph (DAG). These are a hip new trend for thinking about causal inference, so new and trendy that they aren’t really in any mainstream textbooks yet!

DAGS and DAG rules (front doors, back doors, colliders, mediators, etc.) will allow you to visually map the causal relationships between variables and describe to you the variables you must control for in order to properly identify the causal effect you are trying to measure. I show you a simply tool, daggity.net that will help you do this, as well as ggdag in R.