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I am not acquainted with Pearl's approach for causal inference. From what I have seen so far, the causality is inferred from directed acyclic graphs(DAGs).

Rubin's Causal Inference Sec 7.5 proved a theorem stating that asymptotic unbiasedness of OLS estimator for superpopulation treatment effect.

By Rubin, if sample is so large that we have very small bias, the estimation of treatment effect can be done by using OLS with a few covariates. From this, under large sample assumption, I can just perform ordinary linear regression to estimate treatment effect.

If one is inferring such treatment effect, why does one need DAGs to estimate treatment effect as compared to the asymptotic unbiasedness provided by Rubin's result? It seems to me that DAGs should be a special case of Rubin's theorem.

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    $\begingroup$ The theorem in Section 7.5 starts with "Suppose we conduct a completely randomized experiment." This is very much a special case, and not a general result about OLS. This is where the identifying assumptions represented in the DAG can give you some leverage, though of course you can draw a DAG for the completely randomized case as well. $\endgroup$
    – dimitriy
    Commented Feb 26, 2022 at 2:12
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    $\begingroup$ Applications of DAGs are especially useful to causal inference for observational designs, although they can also useful for RCTs (which also suffer from selection biases to causal inferences), including special cases like Mendelian randomized designs. $\endgroup$
    – Alexis
    Commented Feb 26, 2022 at 4:29
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    $\begingroup$ @Alexis Nice, I had not heard the term Mendelian randomization before. $\endgroup$
    – Galen
    Commented Feb 26, 2022 at 4:43
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    $\begingroup$ If nothing else, DAGs and the backdoor criterion identify confounders. If you can't figure out what is a confounder and what isn't, you're flying blind. I view this, indeed, as one of the CHIEF benefits of the causal DAG approach. It is also non-parametric, which makes it fairly robust. It does not depend on ignorability, either - a difficult assumption to verify. $\endgroup$
    – Adrian Keister
    Commented Feb 26, 2022 at 16:13
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    $\begingroup$ A DAG is a graph that encodes some assumptions about causality. It’s not an estimation method, so it’s not semi-parametric or efficient or biased in finite samples. It’s very strange to me to compare a DAG to OLS. $\endgroup$
    – dimitriy
    Commented Feb 26, 2022 at 17:12

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