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Caliper matching permits a candidate matching 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 $|\mathrm{logit}e(X_i)-\mathrm{logit}e(X_j)|\le c$. These are different distances; the numeric tolerance must be interpreted on the selected scale.^[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, and account for the paired or reused-control structure in statistical inference.

Peter C. Austin develops methods for observational studies, including propensity score matching. In his simulation study of caliper matching, treated and untreated people are paired only when their scores are sufficiently close.^[ref]

The caliper creates a practical tradeoff: a wider tolerance can retain more pairs but allow larger differences in measured baseline risk; a tighter tolerance can discard people and change the population represented by the comparison. Austin compared resulting bias, mean squared error and confidence interval coverage under specified data-generating scenarios. His numerical recommendations concern those estimands and scenarios, rather than a guarantee that matching removes unmeasured confounding.^[ref]