Synthetic Control under Out-of-Span Common Shocks: Diagnosis, Exposure Balance and Correction
Abstract
Synthetic control relies on pre-treatment fit to balance the unobserved factors that drive untreated outcomes. The argument fails when an observed common shock, such as a commodity price, moves with the latent factors before treatment and departs from them afterwards and pre-treatment fit then says almost nothing about the synthetic unit's exposure to the shock. I derive a period-specific bound that links the post-treatment bias of any weighting estimator to pre-treatment misfit through a leverage statistic, and show that the statistic decomposes exactly into a latent-factor component and the partial leverage of the observed shock. The decomposition yields a diagnostic for such silent factor that uses no post-treatment outcome of the treated unit. Balancing an observed exposure index removes the problem, but simplex weights can achieve balance only when the treated unit lies inside the donors' exposure hull. Outside the hull, every simplex-weighted estimator carries an exposure imbalance with an explicit lower bound. For that case I propose an exposure-augmented synthetic control that corrects the remaining imbalance with a cross-donor regression, characterise what the correction identifies and when it fails, and derive bias-aware confidence intervals with a breakdown value. Monte Carlo experiments, including designs in which the correction's assumptions fail, map its gains and its limits. Iran's 2012 sanctions coincided with the 2014 oil collapse, and Iran is more oil-dependent than any of its natural comparators. The 2012-15 output loss of about 12 percent survives every adjustment. The persistent loss that standard synthetic control reports after 2016 does not. Any adjustment for oil exposure removes it, and the long-run effect is not identified with these comparators.
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BibTeX
@misc{spruk2026synthetic,
title = {{Synthetic Control under Out-of-Span Common Shocks: Diagnosis, Exposure Balance and Correction}},
author = {Rok Spruk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05535},
eprint = {2610.05535},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05535},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Synthetic Control under Out-of-Span Common Shocks: Diagnosis, Exposure Balance and Correction
AU - Rok Spruk
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05535
UR - https://arxiv.org/abs/2610.05535
AB - Synthetic control relies on pre-treatment fit to balance the unobserved factors that drive untreated outcomes. The argument fails when an observed common shock, such as a commodity price, moves with the latent factors before treatment and departs from them afterwards and pre-treatment fit then says almost nothing about the synthetic unit's exposure to the shock. I derive a period-specific bound that links the post-treatment bias of any weighting estimator to pre-treatment misfit through a leverage statistic, and show that the statistic decomposes exactly into a latent-factor component and the partial leverage of the observed shock. The decomposition yields a diagnostic for such silent factor that uses no post-treatment outcome of the treated unit. Balancing an observed exposure index removes the problem, but simplex weights can achieve balance only when the treated unit lies inside the donors' exposure hull. Outside the hull, every simplex-weighted estimator carries an exposure imbalance with an explicit lower bound. For that case I propose an exposure-augmented synthetic control that corrects the remaining imbalance with a cross-donor regression, characterise what the correction identifies and when it fails, and derive bias-aware confidence intervals with a breakdown value. Monte Carlo experiments, including designs in which the correction's assumptions fail, map its gains and its limits. Iran's 2012 sanctions coincided with the 2014 oil collapse, and Iran is more oil-dependent than any of its natural comparators. The 2012-15 output loss of about 12 percent survives every adjustment. The persistent loss that standard synthetic control reports after 2016 does not. Any adjustment for oil exposure removes it, and the long-run effect is not identified with these comparators.
ER -