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I am looking for a good article, blog post, or text that situates the key 'high-level' differences and agreements between the kinds of counterfactual formal causal reasoning championed by Pearl, Hernán & Robins, and Glymour (i.e. 'structural causal models'), with, say, Imbens' and Rubin's work with potential outcomes.

I am trying to situate some of the formal causal reasoning stuff in the econometrics world with respect to the counterfactual formal causal inference I am more familiar with (Pearl, etc.) without having to work my way through everything Imbens, Rubin and Angrist ever wrote. :)

Has there been a good compare & contrast written?

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Take a look at Section 4 for a comparison of PO and DAG/SCM approaches:

Imbens, Guido W. 2020. "Potential Outcome and Directed Acyclic Graph Approaches to Causality: Relevance for Empirical Practice in Economics." Journal of Economic Literature, 58 (4): 1129-79 https://doi.org/10.1257/jel.20191597 (ungated draft)

Pearl's response can be found at Pearl, J. On Imbens’s Comparison of Two Approaches to Empirical Economics. (2020). Academic blog. Causal Analysis in Theory and Practice. Posted January 29, 2020.

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  • $\begingroup$ +1, I thought the same paper; but were you surprised by that response? $\endgroup$
    – usεr11852
    Commented Jan 5, 2022 at 0:32
  • $\begingroup$ @usεr11852 What did you find surprising? $\endgroup$
    – dimitriy
    Commented Jan 5, 2022 at 0:37
  • $\begingroup$ Nothing really. I found it absolutely predictable. (Like even the existence of it.) $\endgroup$
    – usεr11852
    Commented Jan 5, 2022 at 0:41
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    $\begingroup$ @Alexis I just read his book for fun and it struck me that he is frequently critizing statistics in general or other statisticians but in the entire book he not even once talked about limitations of his theories or explained what they can or cannot do. His answer to the criticism felt the same, every single point is answered with 'this is not true'. $\endgroup$
    – quarague
    Commented Jan 5, 2022 at 19:12
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    $\begingroup$ @quarague Might could be he's correct, and there's not actually a good critique of structural causal models in the offing? $\endgroup$
    – Alexis
    Commented Jan 5, 2022 at 19:21
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We have a unifying theory for potential outcomes, graphical models, and structural econometrics. It is based on the theory of structural causal models.

Check out:

These answers may also help:

Which Theories of Causality Should I know?

Is the linearity assumption in linear regression merely a definition of $\epsilon$?

The references above concern a unified mathematical framework for the counterfactual and structural theories of causation.

In practice, of course, each "school" may have different conventions and cultural differences. For instance, certain identification strategies are more popular in economics than epidemiology, or inside econometrics itself there is a cultural division between "reduced form" and "structural" econometrics, etc.


As for Pearl's answer to Imbens' article, it is simply stating that there's no such thing as a "DAG approach." The formal mathematical framework is a structural causal model. The DAG is just one tool for partially specifying a structural model, namely, imposing certain types of exclusion and independence restrictions. You can impose as many assumptions as you would like, and monotonicity has nothing special in it. For instance, see how Pearl and I defined monotonicity here. That is why it makes no sense to ask how you would represent monotonicity in the "DAG approach" vs "PO approach." Maybe a better question would be: how can we formally represent monotonicity constraints (or other shape constraints) graphically, in a way that we can leverage such constraints to algorithmically derive new identification results? This is the topic of ongoing research.

PS: it goes without saying that I think Imbens is a great scholar, and it has inspired a lot of my own work as well! The above is just a comment on this specific point.

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  • $\begingroup$ +1 Yeah, I am only a few pages in, but Imbens' nattering on$^{*}$ monotonicity made me go "huh wha?" We'll see if he illuminates me. $\endgroup$
    – Alexis
    Commented Jan 5, 2022 at 2:03
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    $\begingroup$ $^{*}$ I have mad respect for Imbens' contributions. $\endgroup$
    – Alexis
    Commented Jan 5, 2022 at 2:03

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