Abstract:
In Wooldridge (2005), I posed a problem whose solution involved showing that the so-called ignorability of treatment assumption, commonly used in the treatment effects literature, was necessarily violated. In particular, in a setting with multiple treatment effects and without distributional or functional form assumptions, I assumed that treatment was randomized with respect to the counterfactual outcomes but not with respect to the covariates. I applied the law of iterated expectations to provide a simple proof that ignorability (given the covariates) necessarily fails.
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