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In step one of judea pearls causal inference book it is to define your graphical causal model. The second step is identification of the estimand for estimation in step 3. Are there any cases where identification may not be possible? i.e. where our dowhy expression cannot be expressed in terms of conditional expectations.

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The causal effect of $X$ on $Y$ is not identifiable in a number of cases. Pearl's Causality: Models, Reasoning, and Inference, 2nd Ed. (2009), on p. 90, has three examples. The simplest possible such example is the graph consisting of two vertices $X\to Y$ with also a confounding bow between $X$ and $Y$ (represented by bidirectional dashed arrows). In such a case, a do expression will not be reducible to an expression containing only conditional expressions that you can evaluate from the (right) data.

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  • $\begingroup$ Note that the confounding bidirected edge signifies an unobserved confounder. The assumption of "no unobserved confounders" is generally necessary to identify a causal estimand in terms of the known variables. $\endgroup$
    – Scriddie
    Commented May 31, 2023 at 10:01
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    $\begingroup$ True, although sometimes a front-door adjustment or instrumental variable can be used to get around that. $\endgroup$ Commented May 31, 2023 at 12:51

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