Synthetic Interventions: Extending Synthetic Controls to Multiple Treatments
Anish Agarwal, Devavrat Shah, Dennis Shen
Operations Research · 2026 · Volume 74 · Issue 2
Abstract
The synthetic controls ( SC ) methodology is a prominent tool for policy evaluation in panel data applications, typically grounded in a low-rank matrix factor model where potential outcomes are governed by low-dimensional latent factors over units and time. In this article, we present the synthetic interventions ( SI ) framework, an extension of the SC framework to accommodate multiple interventions. Fundamental to SI is a low-rank tensor factor model that builds on the matrix structure by embedding a latent factorization over interventions within the temporal factors, and assuming that unit-level latent factors are shared across both time and interventions. To operationalize this framework, we generalize standard SC -based estimators by borrowing strength across interventions, all while preserving their core principles. We establish consistency for one estimator variant and show that a bias-corrected version achieves asymptotic normality, thereby enabling valid inference. Our statistical results are supported by simulation studies and an empirical revisit of a canonical SC tobacco control case study, where we explore related questions not previously examined. Supplemental Material: All supplemental materials, including the code, data, and files required to reproduce the results, are available at https://doi.org/10.1287/opre.2025.1590 .
Keywords
Machine Learning and Data Science, tensor completion, principal component regression, covariate shift
Enable JavaScript for citation tools and additional paper interactions.