= Caliper matching
<Caliper matching> permits a candidate <matching (statistics)> pair only when a prespecified <distance> is at most a tolerance $c$. For <propensity score> $e(X)$, possible rules are $|e(X_i)-e(X_j)|\le c$ or $|\operatorname{logit}e(X_i)-\operatorname{logit}e(X_j)|\le c$. These are different <distances>; the numeric tolerance must be interpreted on the selected scale.<Optimal caliper widths for propensity-score matching when estimating differences in means and differences in proportions in observational studies by Peter C. Austin>[Abstract and section 1: propensity-score calipers and logit-scale matching]{ref}
For a treated unit with <propensity score> $0.40$, a raw-score caliper $c=0.03$ admits a control with score $0.42$ and excludes one with score $0.46$. The matching algorithm still has to choose among admissible controls and decide whether controls may be reused. A tighter caliper excludes distant pairs but can leave more treated units unmatched. Excluding those units changes the population represented by the matched estimate; a caliper is not a guarantee of an unchanged <average treatment effect on the treated>. Check <covariate balance> after <matching (statistics)>, and account for the paired or reused-control structure in <statistical inference>.
Back to article page
