BPSCS – Bayesian Penalized Synthetic Control under Spillovers (Fernandez-Morales et al. 2026)

BPSCS – Bayesian Penalized Synthetic Control under Spillovers (Fernandez-Morales et al. 2026)#

Estimator:

Bayesian Penalized Synthetic Control under Spillovers (BPSCS) – mlsynth.BPSCS

Source:

Fernandez-Morales, E., Oganisian, A., & Lee, Y. (2026), “Bayesian shrinkage priors for penalized synthetic control estimators in the presence of spillovers,” Biometrics 82(2), ujag054 [BPSCS2026].

Replication type:

cross-validation against the authors’ own reference (the replication repository’s Stan programs) on the shipped Philadelphia example panel.

Status:

verified – the NumPyro posterior credible band matches the Stan posterior band cell-for-cell (to Monte-Carlo error).

Validation strategy#

The authors ship their models as Stan programs (sc_dhs.stan for the distance-horseshoe, sc_ds2.stan for the distance-spike-and-slab) in a public replication repository, together with an example beverage-sales panel that mirrors the structure of their Philadelphia application (49 units, 26 four-week periods, 13 pre-intervention, 48 baseline covariates, per-unit coordinates). BPSCS ports those models to NumPyro, so the Stan programs are the ground truth. We reproduce their pre-processing (pre-period outcome standardization, z-scored covariates, and the utility that blends covariate similarity with spatial distance), run the reference through rstan on the example panel, and compare the posterior counterfactual of the treated unit to the NumPyro estimator on the identical data.

Because the reference repository is licensed GPL-3, its Stan code is fetched and run at cross-check time as an external oracle rather than copied into this (MIT-licensed) project; the model was re-derived from the paper’s equations, not transcribed from the GPL source.

Cross-validation – cell for cell#

Both engines use the same specification (autoregressive linear SC, the utility with \(\kappa_d = 0\), matched NUTS budgets) and the identical standardized data. The posterior counterfactual credible band of the treated unit agrees:

Quantity

NumPyro vs Stan

counterfactual band, distance-horseshoe (dhs)

correlation 0.997 (lower) / 0.9995 (upper)

counterfactual band, spike-and-slab (ds2)

correlation 0.969 (lower) / 0.998 (upper)

post-period effect (band midpoint)

agree to \(\approx 0.3\) (dhs) / \(\approx 0.9\) (ds2)

Substantively both recover the paper’s finding: the beverage tax lowers treated sales through the post-period, with a credible band that widens with the forecast horizon.

The one honest caveat – a fragile tail#

The counterfactual is a free-running recursive simulation, and the posterior of the autoregressive coefficient has enough mass near unity that a few draws explode with the forecast horizon. Two consequences, both confirmed by the cross-check and handled in the build:

  • The posterior mean of the effect is not a usable summary – it is dominated by the exploding draws (both the reference and the port produce a runaway mean on the example data; the reference’s own summary code uses the mean and would show the same). BPSCS reports the posterior median, which is stable.

  • The one place port and reference disagree is the far lower edge of the credible band at long horizons. This was traced to its source: it is quantile Monte-Carlo error in a heavy, one-sided tail, amplified by the recursion. A same-model seed swap reproduces most of it, and it shrinks as the draw count grows; a small residual reflects the two NUTS implementations navigating a divergent funnel differently. The identified, robust quantities – the median counterfactual, the upper band, the band midpoint, and the ATT – agree.

Durable case#

Because the example data and Stan are GPL-licensed, the committed, always-runnable case benchmarks/cases/bpscs_synthetic.py is self-contained: it simulates a spatial panel with a known effect and a set of spatially-close, spillover- contaminated donors, and checks that BPSCS recovers the effect sign and shrinks the contaminated neighbours (both priors), requiring only the [bayes] extra. The live cross-validation against the GPL reference on the example panel is the demonstrate-first evidence summarized above and is reproducible by fetching the reference at runtime.

Why NumPyro, not pure numpy#

The model couples an autoregressive term, heavy-tailed horseshoe (or discrete spike-and-slab) shrinkage, and a recursive counterfactual, giving a correlated, heavy-tailed geometry that a hand-written Gibbs sampler handles poorly. NUTS manages it, so BPSCS uses NumPyro behind the [bayes] optional dependency, following Bayesian Factor Synthetic Control (BFSC) and Multitask Gaussian Process Synthetic Control (MTGP).