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Abstract:
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"Common support", the assumption that propensity scores are bounded away from 1, is so named because for large samples it entails that the propensity support of the treatment group be contained within that of the control group. This entailment may appear to be simple to check, but it is not: it refers to true propensity scores, not estimates of them; and even if true propensity score supports coincide supports on the estimated propensity often will not. The naive method of discarding those members of the treatment group whose estimated propensity scores fall above all the controls', and those members of the control group whose propensity scores fall below all those estimated within the treatment group, is needlessly wasteful of sample size.
It is possible to address common support by restricting the range of the estimated propensity score within which comparisons are permitted, but this requires careful determination of the tolerance enforced for matching discrepancies; available heuristics and guidelines attend only to some of the issues that must be considered. I present a new formula for determining caliper widths for matching based on propensity scores.
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