Spatial Coarsened Exact Matching (Spatial CEM)

Standard CEM matches on any set of observed covariates. Spatial CEM explicitly includes geographic covariates — such as region, urban-rural classification, distance deciles, or spatial cluster indicators — as mandatory matching dimensions. This ensures matched pairs are both observationally and geographically comparable, controlling for location-based confounding that standard CEM would ignore if spatial variables were not included.

Bins should reflect substantively meaningful geographic strata set before looking at outcomes — for example, administrative regions, urban-suburban-rural classification, or distance quartiles from a landmark. Avoid data-driven bin selection that maximises matched sample size, as this introduces specification searching. Sensitivity analyses across plausible coarsening schemes are recommended to assess robustness.

Large pruning means the treated and control covariate distributions overlap only in a narrow region of the geographic-covariate space. The resulting ATT is valid for that overlapping subpopulation but may not generalise to all treated areas. Report the fraction pruned and characterise how retained and pruned treated units differ, so readers understand the scope of inference.

Yes, if residuals are spatially autocorrelated within matched strata. After matching, test for residual spatial autocorrelation (e.g., Moran's I on residuals). If significant, cluster standard errors at the spatial block or geographic unit level, or use spatial HAC estimators. Ignoring spatial autocorrelation leads to anti-conservative inference.

No — like all standard matching estimators, Spatial CEM assumes the Stable Unit Treatment Value Assumption (SUTVA): a unit's outcome depends only on its own treatment status. If treated areas generate externalities in neighbouring control areas (e.g., displacement effects, knowledge spillovers), the control group outcomes are contaminated. In such cases, consider spatial difference-in-differences with spillover-robust estimators, or define geographic buffers that exclude potentially contaminated control units.