Consistency and matching without replacement
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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.
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