= 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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