Convex Hull Restriction
In the synthetic control method the counterfactual is built as a weighted average of donor-pool units whose weights are restricted to be non-negative and to sum to one. This confines the comparison unit to the convex hull of the donors, so it cannot extrapolate beyond the support of the observed controls — unlike regression, which can be written as a weighting estimator whose weights sum to one but are not bounded in [0,1] and therefore extrapolate. The price is that a good fit requires the treated unit’s characteristics to lie inside (or near) the donor convex hull; otherwise the weights leave a large gap, and forcing a fit across dissimilar units produces interpolation bias. Weights are typically sparse.
Relied on by
Synthetic control method (SCM) for comparative case studies.