"As Philip Dawid once said "a causal model is just an ambitious associational model". A carefully-considered regression model, with an appropriate set of potential confounders (possibly identified using a causal diagram – see below) measured and included as covariates, is the most appropriate causal model in many simple settings."

http://csm.lshtm.ac.uk/themes/causal-inference/

To paraphrase Angrist and Pischke:

To the extent that the population CEF that it is estimating is causal, so is linear regression. (And that includes LPMs)

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