We need to bring “ignorable treatment assignment” back it into our vocabulary
Unconfoundedness, conditional independence, and ignorable treatment assignment
What’s the difference between unconfoundedness and ignorability? Mathematically, best I can tell, nothing. The phrase conditional independence, which I think Angrist and Pischke used more often or maybe first, is more or less synonyms for both. They all have the same notation:
(y0,y1) _||_ D | X
But in some ways, I think something important has been lost moving away from the word ignorability. And in this essay, I’m going to explain why. In a nutshell, unfoundedness is what we mean when we say that all the problematic confounders are known and quantified. In a DAG, it’s the observed parent variable in that familiar triangle linking treatment and outcome. Unconfoundedness is what allows us to include covariates and avoid omitted variable bias. Uncondoundedness in other words is about possessing in your dataset the known and quantified confounders whic…
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