The paper demonstrates that the matching estimator is not generally consistent for the average treatment effect of the treated when the matching is done without replacement using propensity scores . To achieve consistency, practitioners must either assume that no unit exists with a propensity score greater than one-half or assume that there is no confounding among such units. Illustrations suggest that the result applies also to matching using other metrics as long as it is done without replacement.
The paper shows that matching without replacement on propensity scores produces estimators that generally are inconsistent for the average treatment effect of the treated . To achieve consistency, practitioners must either assume that no units exist with propensity scores greater than one-half or assume that there is no confounding among such units. The result is not driven by the use of propensity scores, and similar artifacts arise when matching on other scores as long as it is without replacement.
R
demonstrates that the matching estimator is not generally consistent
shows that matching without replacement on propensity scores produces estimators that generally are inconsistent
D
when the matching is done without replacement using propensity scores
R
unit exists with a propensity score
units exist with propensity scores
R
Illustrations suggest that the result applies also to matching using other metrics
The result is not driven by the use of propensity scores, and similar artifacts arise when matching on other scores
D
done