# Non-parametric identifiability and sensitivity analysis of synthetic control models

arXiv: https://arxiv.org/abs/2301.07656 · HTML: https://mlsanity.com/paper/2301.07656/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 36 references that are in the map.
- First posted on arXiv 18 Jan 2023.

## Builds on (most cited first, 18 of 18)

- [Representation Learning via Invariant Causal Mechanisms](https://mlsanity.com/paper/2010.07922/) (2020)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Learning Independent Causal Mechanisms](https://mlsanity.com/paper/1712.00961/) (2017)
- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Out-of-distribution Generalization with Causal Invariant Transformations](https://mlsanity.com/paper/2203.11528/) (2022)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [Invariant Causal Mechanisms through Distribution Matching](https://mlsanity.com/paper/2206.11646/) (2022)
- [D'ARTAGNAN: Counterfactual Video Generation](https://mlsanity.com/paper/2206.01651/) (2022)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Sense and Sensitivity Analysis: Simple Post-Hoc Analysis of Bias Due to Unobserved Confounding](https://mlsanity.com/paper/2003.01747/) (2020)
- [Integrating overlapping datasets using bivariate causal discovery](https://mlsanity.com/paper/1910.11356/) (2019)
- [On the Assumptions of Synthetic Control Methods](https://mlsanity.com/paper/2112.05671/) (2021)
- [The Proximal ID Algorithm](https://mlsanity.com/paper/2108.06818/) (2021)
- [Disentangling Causal Effects from Sets of Interventions in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2210.05446/) (2022)
- [Leveraging directed causal discovery to detect latent common causes](https://mlsanity.com/paper/1910.10174/) (2019)
- [Theory for identification and Inference with Synthetic Controls: A Proximal Causal Inference Framework](https://mlsanity.com/paper/2108.13935/) (2021)
- [Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables](https://mlsanity.com/paper/1506.03880/) (2015)
- [MultiVerse: Causal Reasoning using Importance Sampling in Probabilistic Programming](https://mlsanity.com/paper/1910.08091/) (2019)

## Built on by (most cited first, 5 of 5)

- [Contrastive representations of high-dimensional, structured treatments](https://mlsanity.com/paper/2411.19245/) (2024)
- [Spillover Detection for Donor Selection in Synthetic Control Models](https://mlsanity.com/paper/2406.11399/) (2024)
- [Local Interference: Removing Interference Bias in Semi-Parametric Causal Models](https://mlsanity.com/paper/2503.18756/) (2025)
- [Quantum oracles give an advantage for identifying classical counterfactuals](https://mlsanity.com/paper/2512.13692/) (2025)
- [Targeted Synthetic Control Method](https://mlsanity.com/paper/2602.04611/) (2026)

## Abstract (arXiv)

Quantifying cause and effect relationships is an important problem in many domains. The gold standard solution is to conduct a randomised controlled trial. However, in many situations such trials cannot be performed. In the absence of such trials, many methods have been devised to quantify the causal impact of an intervention from observational data given certain assumptions. One widely used method are synthetic control models. While identifiability of the causal estimand in such models has been obtained from a range of assumptions, it is widely and implicitly assumed that the underlying assumptions are satisfied for all time periods both pre- and post-intervention. This is a strong assumption, as synthetic control models can only be learned in pre-intervention period. In this paper we address this challenge, and prove identifiability can be obtained without the need for this assumption, by showing it follows from the principle of invariant causal mechanisms. Moreover, for the first time, we formulate and study synthetic control models in Pearl's structural causal model framework. Importantly, we provide a general framework for sensitivity analysis of synthetic control causal inference to violations of the assumptions underlying non-parametric identifiability. We end by providing an empirical demonstration of our sensitivity analysis framework on simulated and real data in the widely-used linear synthetic control framework.