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Statistics and causal inference?

In his 1984 paper "Statistics and Causal Inference", Paul Holland raised one of the most fundamental questions in statistics:

What can a statistical model say about causation?

This led to his motto:

NO CAUSATION WITHOUT MANIPULATION

which emphasized the importance of restrictions around experiments that consider causation. Andrew Gelman makes a similar point:

"To find out what happens when you change something, it is necessary to change it."...There are things you learn from perturbing a system that you'll never find out from any amount of passive observation.

His ideas are summarized in this article.

What considerations should be made when making a causal inference from a statistical model?