# Theory for identification and Inference with Synthetic Controls: A Proximal Causal Inference Framework

arXiv: https://arxiv.org/abs/2108.13935 · HTML: https://mlsanity.com/paper/2108.13935/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2021.

## Built on by (most cited first, 9 of 9)

- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Proximal Causal Learning of Conditional Average Treatment Effects](https://mlsanity.com/paper/2301.10913/) (2023)
- [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)
- [Proximal Path-Specific Inference](https://mlsanity.com/paper/2605.09462/) (2026)
- [Are Synthetic Control Weights Balancing Score?](https://mlsanity.com/paper/2211.01575/) (2022)
- [Balanced Filtering via Disclosure-Controlled Proxies](https://mlsanity.com/paper/2306.15083/) (2023)
- [Targeted Synthetic Control Method](https://mlsanity.com/paper/2602.04611/) (2026)
- [Spatiotemporal Proximal Causal Inference under Hidden Confounding and Interference](https://mlsanity.com/paper/2608.01352/) (2026)

## Abstract (arXiv)

Synthetic control (SC) methods are commonly used to estimate the treatment effect on a single treated unit in panel data settings. An SC is a weighted average of control units built to match the treated unit, with weights typically estimated by regressing (summaries of) pre-treatment outcomes and measured covariates of the treated unit to those of the control units. However, it has been established that in the absence of a good fit, such regression estimator will generally perform poorly. In this paper, we introduce a proximal causal inference framework to formalize identification and inference for both the SC and ultimately the treatment effect on the treated, based on the observation that control units not contributing to the construction of an SC can be repurposed as proxies of latent confounders. We view the difference in the post-treatment outcomes between the treated unit and the SC as a time series, which opens the door to various time series methods for treatment effect estimation. The proposed framework can accommodate nonlinear models, which allows for binary and count outcomes that are understudied in the SC literature. We illustrate with simulation studies and an application to evaluation of the 1990 German Reunification.