Title: A note on adapting propensity score matching and selection models to choice based samples
Description: "The probability of selection into treatment plays an important role in matching and selection models.  However, this probability can often not be consistently estimated, because of choice-based sampling designs with unknown sampling weights.  This note establishes that the selection and matching procedures can be implemented using propensity scores fit on choice-based samples with misspecified weights, because the odds ratio of the propensity score fit on the choice-based sample is monotonically related to the odds ratio of the true propensity scores"--National Bureau of Economic Research web site.