S3E27: Propensity Scores -- I Meant To Do That!
Quantitude
How Much Fuzz Is There in Propensity Scores?
Theorems of propensity scores all assume that you have the true propensity score for each individual, which we don't. So they need to be estimated and can achieve balance if estimates are done well. Most matching algorithms do not consider how close is close; they just find the closest. If i have an extreme propensity score and there's no control unit with a close propensity score, i will be paired with someone who is very far from me. That is that fuzz that you are talking about, where we're not really twins even on the propensity score let alone on the covers. And it turns out using a caliper tends to dramatically improve the forensics results.
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