Controlling for Z will partially control for it's causal factor W - which is a mediator along the path we're trying to estimate. This will bias our estimate. Thus Z is a bad control.

University of Michigan - Ann Arbor

Common Bad Controls

Cinelli, Carlos, et al. “A Crash Course in Good and Bad Controls.” Technical Report -UCLA, 21 Mar. 2020.

https://ftp.cs.ucla.edu/pub/stat_ser/r493.pdf

A Crash Course in Good and Bad
Controls

Z is a mediator along the path that we're trying to estimate. Controlling for Z will adversely impact our estimation.
Thus Z is a bad control.

Bad Control I

Bad Control II

Controlling for Z will not stop the confounding effect of U on X and Y. Z is thus a bad control. 

Bad Control III

This is the M-bias diagram.
Z blocks the confounding effects of U1 and U2 on X and Y. Controlling for Z stops the blocking - and thus opens up a backdoor path with confounding factors U1 and U2 in an otherwise unbiased diagram.

Learn Before

Related