Propensity Score Calipers and the Overlap Condition

Ben Hansen
Professor of Education and Statistics, University of Michigan
Apr 27 12:00pm - 1:30pm

Propensity scores (Rosenbaum and Rubin, 1983) are used widely to address measured confounding in quasiexperiments. They also arise in connection with the antecedent question of whether non-equivalent treatment and control groups are suitable for comparison at all, with or without covariate adjustments. 

"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 few methodologists who have addressed the issue have tended to do so by changing the subject, specifying sample trimming rules suited to technical objectives other than the straightforward one of ensuring that like be compared to like (Crump et al, 2009; Rosenbaum 2012).  I suggest an alternate approach based on caliper matching, using a novel procedure to determine the value of the caliper.  I'll discuss two examples, one from education and the other from sociology and public health.