Is it conceivable for the treated units to have propensity scores systematically lower than those estimated for the control units?
Thanks in advance.
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This would likely indicate a poor-fitting propensity score model. The propensity score model should model the true probability of receiving treatment, and if the predictions are poor (i.e., those predicted to receive treatment actually receive control), this might be indicative of a bad model. Remember, though, that the point of propensity scores is to achieve balance. If you can achieve balance even with these oddly performing propensity scores, then it doesn't matter whether they do a good job at representing the actual probability fo treatment. The C-statistic, a measure of how good the predictions are from a classification model, has been shown to be a poor predictor of the performance of propensity scores, so focus less on their interpretation as probabilities of treatment and more on their potential to balance.
