Models
Synthetic control estimators that let the treatment reach the donor pool
Classical synthetic control assumes SUTVA on the donor pool: whatever happens to the treated unit leaves the controls untouched. When that fails — a tobacco tax that pushes sales across a state line, a secession that travels a trade network, a tramway that redirects footfall one street over — the synthetic counterfactual is built partly from contaminated donors and the estimate is biased. Synthetic control is especially exposed here, because its weights actively select the donors most correlated with the treated unit, and those are often exactly the units the treatment leaks into.
Every model in scspill drops that assumption and reports two estimands:
- \(\xi_{0t}\) — the treatment effect on the treated unit, purged of the contamination; and
- \(\xi_{it}\) — the spillover effect received by donor \(i\), which classical synthetic control cannot express at all.
What the models disagree about is what to assume about the leakage: a spatial process on the donor outcomes, a researcher-specified spillover structure, an inversion of the donors’ own cross-weights, or a partition into exposed and clean clusters. Those assumptions are not nested, which is exactly why it is worth having more than one — run two and they bracket the answer.
Available now
scspill implements one model. Everything under Planned below is a roadmap: none of it is implemented, and none of those method names is accepted. Passing one raises a validation error rather than silently falling back.
| Model | method |
Reference | Class | Page |
|---|---|---|---|---|
| Bayesian spatial-autoregressive spillover SCM | "sar" |
Sakaguchi & Tagawa (2026), The Econometrics Journal, doi:10.1093/ectj/utag006 | SCSPILL |
sar → |
sar — spillovers as a spatial process
sar puts a spatial-autoregressive process on the donor outcomes themselves. The treated unit’s outcome propagates into the donor pool through an exposure vector \(\mathbf w\) you supply, the donors propagate to each other through a matrix \(\mathbf W\) you supply, and a single scalar intensity \(\rho\) — estimated, not assumed — scales the whole channel. Under a perfect pre-treatment fit with unconstrained weights \(\boldsymbol\alpha\), both estimands are identified in closed form from \((\boldsymbol\alpha, \rho, \mathbf w, \mathbf W)\) alone; covariate coefficients, latent factors, and error variances cancel out. Inference is a two-step Bayesian sampler, so every quantity arrives with a posterior rather than an asymptotic approximation. At \(\rho = 0\) the model collapses exactly to the Bayesian horseshoe synthetic control, so the no-spillover case is nested rather than assumed away.
Reach for it when you can defend a spatial or network weighting a priori (contiguity, trade volumes, distance decay), you want the per-donor spillover as an object of interest rather than a nuisance, and you want honest uncertainty on a weakly identified intensity. Look elsewhere when you cannot motivate \((\mathbf w, \mathbf W)\), when only a handful of donors are exposed and dropping them is cheap, or when your pre-period is too short to pin \(\rho\) down — \(\rho\) is this model’s weakly identified parameter, and no amount of sampling changes that.
Full statement of the model, the identification theorem, the samplers, and the six documented departures from the authors’ R replication package are on the sar page.
Planned
The three models below are candidates, not features. They are listed so the package’s intended scope is legible and so the method names stay coherent — none of them exists in scspill today, and there is no release date.
| Model | Reserved method |
Reference | How it would identify the spillover |
|---|---|---|---|
| SCM with spillover effects | "cd" |
Cao & Dowd, arXiv:1902.07343 (2019, rev. 2026) | Keep the exposed donors and impose a researcher-specified spillover-structure matrix, linear in unknown parameters, recovering direct and per-unit spillover effects jointly. Comes with a misspecification test for the structure you assumed. |
| Inclusive synthetic control | "iscm" |
Di Stefano & Mellace, arXiv:2403.17624 (2024) | Keep the exposed donors with no parametric spillover structure at all: build a synthetic control for every affected unit, then invert the system of their own cross-weights to de-contaminate the gaps. |
| Partial-interference synthetic control group | "grossi" |
Grossi, Mariani, Mattei, Lattarulo & Öner (2025), JRSS-A 188(1):223–240, arXiv:2004.05027 | Drop the treated unit’s whole cluster from the pool and rebuild from the far, clean clusters only. Cleanest identification when partial interference is defensible, at the cost of pre-treatment fit. |
In one line each: sar models the leakage and estimates its intensity; cd keeps the contaminated donors and assumes a structure it can test; iscm keeps them and inverts the data’s own cross-weights; grossi drops them and identifies off a cluster partition.
Relationship to mlsynth
scspill’s estimator architecture follows mlsynth — a pydantic config in, a standardized results object out — and the four models above are exactly the four its SPILLSYNTH dispatcher exposes as method="sar" | "cd" | "iscm" | "grossi". The names here are deliberately identical, so moving between the two libraries is a rename rather than a rewrite. Where scspill goes further is depth: it carries the sar model’s full appendix machinery — the Geweke joint distribution test, prior sensitivity grids, prior predictive checks, a Monte Carlo engine, and a benchmark suite pinned to the authors’ frozen R results.
References
- Sakaguchi, S., & Tagawa, H. (2026). Identification and Bayesian Inference for Synthetic Control Methods with Spillover Effects. The Econometrics Journal. https://doi.org/10.1093/ectj/utag006
- Cao, J., & Dowd, C. (2019, rev. 2026). Estimation and Inference for Synthetic Control Methods with Spillover Effects. https://arxiv.org/abs/1902.07343
- Di Stefano, R., & Mellace, G. (2024). The Inclusive Synthetic Control Method. https://arxiv.org/abs/2403.17624
- Grossi, G., Mariani, M., Mattei, A., Lattarulo, P., & Öner, Ö. (2025). Direct and spillover effects of a new tramway line on the commercial vitality of peripheral streets: a synthetic-control approach. Journal of the Royal Statistical Society Series A 188(1):223–240. https://arxiv.org/abs/2004.05027