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Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder

arXiv 1609.08816 ↗First posted 28 Sep 2016stat.MEcited by 138

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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.

Key facts. Cited by 138 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Sep 2016.

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Citing papers per year: 2021: 25; 2022: 22; 2023: 29; 2024: 19; 2025: 19; 2026: 24.

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  1. 2022A Review of Off-Policy Evaluation in Reinforcement Learningcited by 92
  2. 2021Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restrictioncited by 54
  3. 2021Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachcited by 43
  4. 2023A Survey on Causal Reinforcement Learningcited by 43
  5. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  6. 2021Proximal Reinforcement Learning: Efficient Off-Policy Evaluation in Partially Observed Markov Decision Processescited by 40
  7. 2021Deep Proxy Causal Learning and its Application to Confounded Bandit Policy Evaluationcited by 39
  8. 2021Causal Effect Inference for Structured Treatmentscited by 38
  9. 2021Transporting Causal Mechanisms for Unsupervised Domain Adaptationcited by 38
  10. 2021Instrumental Variable Value Iteration for Causal Offline Reinforcement Learningcited by 35
  11. 2021A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processescited by 34
  12. 2024Applied Causal Inference Powered by ML and AIcited by 30
38 more
  1. 2021A Critical Look at the Consistency of Causal Estimation With Deep Latent Variable Modelscited by 29
  2. 2022Long-term Causal Inference Under Persistent Confounding via Data Combinationcited by 27
  3. 2022Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processescited by 26
  4. 2021Off-Policy Evaluation in Partially Observed Markov Decision Processes under Sequential Ignorabilitycited by 24
  5. 2023Causal Reinforcement Learning: A Surveycited by 22
  6. 2021Proximal Learning for Individualized Treatment Regimes Under Unmeasured Confoundingcited by 21
  7. 2021Minimax Kernel Machine Learning for a Class of Doubly Robust Functionals with Application to Proximal Causal Inferencecited by 20
  8. 2021A Spectral Approach to Off-Policy Evaluation for POMDPscited by 20
  9. 2022Future-Dependent Value-Based Off-Policy Evaluation in POMDPscited by 20
  10. 2022An Instrumental Variable Approach to Confounded Off-Policy Evaluationcited by 20
  11. 2022Off-Policy Evaluation for Episodic Partially Observable Markov Decision Processes under Non-Parametric Modelscited by 18
  12. 2023Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounderscited by 17
  13. 2022Conceptualizing Treatment Leakage in Text-based Causal Inferencecited by 14
  14. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  15. 2022Deep Learning Methods for Proximal Inference via Maximum Moment Restrictioncited by 13
  16. 2022Detecting hidden confounding in observational data using multiple environmentscited by 13
  17. 2025Black Box Causal Inference: Effect Estimation via Meta Predictioncited by 13
  18. 2022Inference on Strongly Identified Functionals of Weakly Identified Functionscited by 12
  19. 2022Spectral Representation Learning for Conditional Moment Modelscited by 12
  20. 2022Adapting to Latent Subgroup Shifts via Concepts and Proxiescited by 12
  21. 2024Spectral Representation for Causal Estimation with Hidden Confounderscited by 12
  22. 2021The Proximal ID Algorithmcited by 11
  23. 2021Intact-VAE: Estimating Treatment Effects under Unobserved Confoundingcited by 10
  24. 2021Causal Mediation Analysis with Hidden Confounderscited by 10
  25. 2022Partial Identification with Noisy Covariates: A Robust Optimization Approachcited by 10
  26. 2023Causal Fairness under Unobserved Confounding: A Neural Sensitivity Frameworkcited by 10
  27. 2021Causal Inference Despite Limited Global Confounding via Mixture Modelscited by 9
  28. 2022Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approachcited by 9
  29. 2021Causal Effect Variational Autoencoder with Uniform Treatmentcited by 8
  30. 2022Causal Inference via Style Transfer for Out-of-distribution Generalisationcited by 8
  31. 2023Causal Discovery from Subsampled Time Series with Proxy Variablescited by 8
  32. 2025DeCaFlow: A deconfounding causal generative modelcited by 8
  33. 2023Proximal Causal Learning of Conditional Average Treatment Effectscited by 7
  34. 2023Debiasing Recommendation by Learning Identifiable Latent Confounderscited by 7
  35. 2023Partial Identification of Causal Effects Using Proxy Variablescited by 7
  36. 2024Proximal Causal Inference With Text Datacited by 7
  37. 2024Media Bias Matters: Understanding the Impact of Politically Biased News on Vaccine Attitudes in Social Mediacited by 7
  38. 2024On the Parameter Identifiability of Partially Observed Linear Causal Modelscited by 7

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