Common Support and Overlap
Summary
Common support is the region where the propensity-score (and covariate) distributions of the treated and control groups overlap. The positivity component of strong ignorability, , requires it. Without overlap, an effect can only be obtained by extrapolation. A key advantage of matching is that it makes a lack of overlap visible — unlike regression/selection models, which silently extrapolate. Analysts restrict to the region of common support, discarding (trimming) units outside the other group’s range.
Overview
Matching methods implicitly assume substantial overlap of the propensity-score distributions. When many controls are very different from all treated units, they are inappropriate comparison points for the ATT. Different matching structures handle overlap differently: nearest-neighbor with calipers automatically uses only units in (or near) the region of common support, whereas subclassification and weighting use all individuals regardless of overlap — so with those it can be beneficial to explicitly restrict to the common-support region.
Main Content
Region of common support ^def-common-support
The region of common support is the range of propensity-score values (or, more generally, the covariate region) represented in both the treated and control groups. Effects can be reliably estimated only within it; outside it, estimation requires extrapolation rather than interpolation. This is the empirical counterpart of the positivity / overlap assumption .
Methods for assessing / enforcing common support ^def-trimming
- Propensity-score trimming: discard individuals with propensity-score values outside the range of the other group.
- Convex hull (King and Zeng, 2006): examine the multidimensional covariate space to identify where comparisons require interpolation vs. extrapolation. Defining the discard rule using one or two key covariates (rather than the propensity score itself) aids interpretation of who is excluded. Calipers in nearest-neighbor matching enforce overlap implicitly.
Common support constrains the estimand ^warn-estimand
Lack of overlap may make the ATE impossible to estimate reliably — e.g., if some controls lie outside the range of treated units, for those controls is unidentified without heavy extrapolation. For the ATT, discarding controls outside the treated range is fine (even beneficial), but discarding treated units changes the group to which the results apply (Crump et al., 2009). Examining common support thus informs the choice between ATT and ATE.
Matching surfaces non-overlap that regression hides ^def-vs-regression
Traditional regression models do not examine the joint distribution of predictors (in particular treatment vs. covariates), so they extrapolate into regions with no support without warning. Matching makes it explicit when the treatment effect cannot be separated from other group differences — a well-specified, highly-interacted outcome regression would reveal the same imbalance, but such models are rarely fit in practice. Selection and regression models perform poorly under insufficient overlap precisely because they do not check it.
Examples
Region-of-common-support trimming on the propensity-score distribution plot (Stuart and Green, 2008): unmatched control units cluster at low propensity-score values entirely outside the treated units’ range; these are discarded so that comparisons rest on interpolation. In the “look forward” guidance, step 3 explicitly directs analysts to examine the common support and its implications for the estimand — asking whether there is enough overlap to estimate the ATE, or whether the ATT can be estimated more reliably.
Connections
- The empirical face of the positivity condition in Propensity Score and the Balancing Property.
- Calipers and weighting handle overlap differently — see Matching Methods and Distance Measures.
- Visualized via the propensity-score distribution plot in Covariate Balance Diagnostics.
- Step 3 of the workflow in Propensity Score Matching - Overview.
- Insufficient overlap is where regression-based fixes for Omitted Variables Bias and The Selection Problem fail; the design-based alternative Synthetic Control faces an analogous support/convex-hull requirement.