# On the Assumptions of Synthetic Control Methods

arXiv: https://arxiv.org/abs/2112.05671 · HTML: https://mlsanity.com/paper/2112.05671/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Dec 2021.

## Built on by (most cited first, 12 of 12)

- [Intervention Generalization: A View from Factor Graph Models](https://mlsanity.com/paper/2306.04027/) (2023)
- [Synthetic Control As Online Linear Regression](https://mlsanity.com/paper/2202.08426/) (2022)
- [Non-parametric identifiability and sensitivity analysis of synthetic control models](https://mlsanity.com/paper/2301.07656/) (2023)
- [Spillover Detection for Donor Selection in Synthetic Control Models](https://mlsanity.com/paper/2406.11399/) (2024)
- [Heterogeneous Synthetic Learner for Panel Data](https://mlsanity.com/paper/2212.14580/) (2022)
- [Asymptotically Unbiased Synthetic Control Methods by Moment Matching](https://mlsanity.com/paper/2307.11127/) (2023)
- [Adaptive Experiment Design with Synthetic Controls](https://mlsanity.com/paper/2401.17205/) (2024)
- [Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls](https://mlsanity.com/paper/2211.15241/) (2022)
- [Weighted Sum-Rate Maximization With Causal Inference for Latent Interference Estimation](https://mlsanity.com/paper/2211.08327/) (2022)
- [Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumption](https://mlsanity.com/paper/2309.16409/) (2023)
- [Compositional Models for Estimating Causal Effects](https://mlsanity.com/paper/2406.17714/) (2024)
- [Targeted Synthetic Control Method](https://mlsanity.com/paper/2602.04611/) (2026)

## Abstract (arXiv)

Synthetic control (SC) methods have been widely applied to estimate the causal effect of large-scale interventions, e.g., the state-wide effect of a change in policy. The idea of synthetic controls is to approximate one unit's counterfactual outcomes using a weighted combination of some other units' observed outcomes. The motivating question of this paper is: how does the SC strategy lead to valid causal inferences? We address this question by re-formulating the causal inference problem targeted by SC with a more fine-grained model, where we change the unit of the analysis from "large units" (e.g., states) to "small units" (e.g., individuals in states). Under this re-formulation, we derive sufficient conditions for the non-parametric causal identification of the causal effect. We highlight two implications of the reformulation: (1) it clarifies where "linearity" comes from, and how it falls naturally out of the more fine-grained and flexible model, and (2) it suggests new ways of using available data with SC methods for valid causal inference, in particular, new ways of selecting observations from which to estimate the counterfactual.