Suppose that worst comes to worst, and our causal model does not permit estimation of the causal effect P(Y | do(X)) from observations alone. Perhaps we also cannot conduct a randomized experiment with random assignment of X. A clever researcher might ask whether we might estimate P(Y | do(X)) by randomizing some other variable, say Z, that is more accessible to control than X. For instance, if we want to assess the effect of cholesterol levels (X) on heart disease (Y), we might be able to manipulate the subjects’ diet (Z) instead of exercising direct control over the cholesterol levels in
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