%0 Report
        %A Heckman, James J.
%A Todd, Petra E.
        %T A Note on Adapting Propensity Score Matching and Selection Models to Choice Based Samples
        %D 2009
        %8 2009 Jul
        %I Institute of Labor Economics (IZA)
        %C Bonn
        %7 IZA Discussion Paper
        %N 4304
        %U https://www.iza.org/index.php/publications/dp4304
        %X 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.
        %K propensity scores
%K matching models
%K choice-based sampling
%K selection models