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@autoregress @yudapearl @Jabaluck Great food for thought, thanks Peter.
If I could elaborate on the empirical setting, I might change in the following way:
X: committed a crime
Z: crime recorded in databases
This highlights that there are two types of error that could occur:
(X = 1, Z = 0) vs. (X = 0, Z= 1).
If I could elaborate on the empirical setting, I might change in the following way:
X: committed a crime
Z: crime recorded in databases
This highlights that there are two types of error that could occur:
(X = 1, Z = 0) vs. (X = 0, Z= 1).
@autoregress @yudapearl @Jabaluck Still consistent with all your points, but might be slightly more empirically relevant in some of the settings (I'm keeping credit records in the back of my mind)
@autoregress @yudapearl @Jabaluck It also helps show why there may be an issue with the front-door here, say vs. the the backdoor. Say there are two "crime registries" that employers use. Z1 and Z2. You as the empirical researcher only observe Z1. I think then, your frontdoor estimate would be wrong, right?
