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How can I compute counterfactuals, given a parametric model for the structural equation for the outcome?
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Brady Neal looks this question in detail on

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In an experimental setting, where a model is not available, and the experimenter must answer interventional questions on the basis of a finite sample of observed individuals, let us analyze an individual named Joe, and assume that the experimenter observes a set of $10$ individuals, with Joe being participant $1$.

Each individual is characterized by a distinct vector $U_i=(U_X, U_H, U_Y)$, as shown in the a table below:

Using this information, we can create a full data set that complies with the model.

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