I’m currently reading this great paper by Carlos Cinelli and Chad Hazlett: “Making Sense of Sensitivity: Extending Omitted Variable Bias”. They develop a full suite of sensitivity analysis tools for the omitted variable problem in linear regression, which everyone interested in causal inference should have a look at. While kind of a side topic, they make an important point on page 6 (footnote 6):
[…] since the researcher’s goal is to estimate the causal effect of D on Y , usually Z is required only to, along with X, block the back-door paths from D to Y (Pearl 2009), or equivalently, make the treatment assignment conditionally ignorable. In this case, could reflect not only its causal effect on Y , if any, but also other spurious associations not eliminated by standard assumptions.