Why ask why? Forward causal inference and reverse causal questions

Why ask why? Forward causal inference and reverse causal questions was written by Andrew Gelman and Guido Imbens in 2013.

The authors discuss two categories of causal questions:

1. Forward causal questions: "if x were changed by one unit, how much would y be expected to change?"

2. Reverse causal inference: "What causes Y?"

Forward causal inference (i.e. y(T=1, x) − y(T=0, x)) is the norm, but a forward causal study is usually motivated by a reverse causal question.

The authors formalize a framework for establishing that there is not a causal relation between a characteristic Z_i and an outcome Y_i within a population homogeneous on characteristics W_i: Y_i ⊥ Z_i | W_i.

The first model that can be fit to this framework supposes that all relevant characteristics are observed. Therefore, after conditioning on W_i, any correlation between Z_i and Y_i is explained by predictors X_i: Y_i(x) ⊥ Z_i | W_i.

The second model supposes that there is an unobserved characteristic V_i, and that any correlation between Z_i and Y_i disappears when conditioning on both the observed and unobserved: Y_i ⊥ Z_i | W_i,V_i.

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