# Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder

arXiv: https://arxiv.org/abs/1609.08816 · HTML: https://mlsanity.com/paper/1609.08816/

## Key facts

- Cited by 139 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Sep 2016.

## Built on by (most cited first, 30 of 139)

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- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
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- [Causal Effect Inference for Structured Treatments](https://mlsanity.com/paper/2106.01939/) (2021)
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- [A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Models](https://mlsanity.com/paper/2102.06648/) (2021)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2205.13589/) (2022)
- [Off-Policy Evaluation in Partially Observed Markov Decision Processes under Sequential Ignorability](https://mlsanity.com/paper/2110.12343/) (2021)
- [Causal Reinforcement Learning: A Survey](https://mlsanity.com/paper/2307.01452/) (2023)
- [Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confounding](https://mlsanity.com/paper/2105.01187/) (2021)
- [A Spectral Approach to Off-Policy Evaluation for POMDPs](https://mlsanity.com/paper/2109.10502/) (2021)
- [Future-Dependent Value-Based Off-Policy Evaluation in POMDPs](https://mlsanity.com/paper/2207.13081/) (2022)
- [Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inference](https://mlsanity.com/paper/2104.02929/) (2021)
- [An Instrumental Variable Approach to Confounded Off-Policy Evaluation](https://mlsanity.com/paper/2212.14468/) (2022)
- [Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Models](https://mlsanity.com/paper/2209.10064/) (2022)
- [Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders](https://mlsanity.com/paper/2303.02320/) (2023)
- [Conceptualizing Treatment Leakage in Text-based Causal Inference](https://mlsanity.com/paper/2205.00465/) (2022)
- [Deep Learning Methods for Proximal Inference via Maximum Moment Restriction](https://mlsanity.com/paper/2205.09824/) (2022)
- [Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Model](https://mlsanity.com/paper/2306.01424/) (2023)
- [Detecting hidden confounding in observational data using multiple environments](https://mlsanity.com/paper/2205.13935/) (2022)
- [Black Box Causal Inference: Effect Estimation via Meta Prediction](https://mlsanity.com/paper/2503.05985/) (2025)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)

## Abstract (arXiv)

We consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the con- founder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014) that rests on identification of the measurement error mechanism. When only one proxy for the confounder is available, or the required rank condition is not met, we develop a strategy to test the null hypothesis of no causal effect.