When is a Control a Bad Control Exactly Hi just had a short question. If a control variable is caused by another control variable would that make it a bad control? I know control is bad if it is the direct outcome of the treatment but in this case, we have it as an outcome of another control.


If a control variable is caused by another control variable would that make it a bad control?

It depends. Let's imagine the following Directed Acyclic Graph (DAG):
$A \rightarrow B \rightarrow C \rightarrow D$ with $A \rightarrow D$. We want to estimate the effect of $A$ in $D$. There is a direct path ($AD$) and the indirect path through the mediators $B$ and $C$ ($ABCD$). We usually want the TOTAL effect, so in this case, it wouldn't be appropriate to control any of the variables. If you want only the direct effect between $A$ and $D$ then it would be appropriate to control for $B$, $C$, or $B$ and $C$. However, this is not the only possibility. Our DAG could also be:
$A \rightarrow B \rightarrow C \leftarrow D$ with $A \rightarrow D$. Adjusting only for $C$ would be bad because it is a collider, but if you adjust for $B$ and $C$ it is fine.
However, these are very simple DAGs. Imagine that we had $A \rightarrow B \rightarrow C \leftarrow D$ with $A \rightarrow D$ but also $A \rightarrow C$ or $A \leftarrow C$. Adjusting for $B$ and $C$ or simply $C$ would be bad because you would open the path $DCA$. With more complex graphs, things will get even more complicated. There is a very good paper on good and bad controls: A Crash Course in Good and Bad Controls.
