IZA DP No. 4304: A Note on Adapting Propensity Score Matching and Selection Models to Choice Based Samples
published in: Econometric Journal, 2009, 12 (Supplement), S230-S234
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.