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Lets assume we want to perform a 'reduced-form' causal analysis to evaluate the impact of a program on the dependent variable of interest. (However the question is more universal).

Lets further assume, that this approach requires controlling for a confounder variable or group of confounders. The variables for this purpose are chosen correctly (assumption, that no bad control, such as overcontrol or control on collider happens).

My intuition suggest, that the estimator of interest (by the program variable) is unbiased only if we perform such control 'correctly'. Some reasons for failing the control I can imagine: not accounting for all required control variables (obvious), measurement error on control variable, proxy control, unobservable control variable, wrong functional form.

As there is many possible reasons for failing in fully controlling for a confounder in a model, my question is: is there a comprehensive 'guide' or a review paper how to perform such control correctly? Or maybe a paper describing what fallacies (and hopefully their consequences) can be made when trying to control for a confounder?

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    $\begingroup$ I recommend Pearl, Glymour, and Jewell's Causal Inference in Statistics: A Primer. Then tackle Causality: Models, Inference, and Reasoning, by Pearl. You'll get a good feel for the possible mistakes to be made once you've worked your way through those books. $\endgroup$ – Adrian Keister Sep 16 '20 at 22:19

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