# Long Story Short: Omitted Variable Bias in Causal Machine Learning

arXiv: https://arxiv.org/abs/2112.13398 · HTML: https://mlsanity.com/paper/2112.13398/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 70 references that are in the map.
- First posted on arXiv 26 Dec 2021.

## Builds on (most cited first, 12 of 12)

- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Interval Estimation of Individual-Level Causal Effects Under Unobserved Confounding](https://mlsanity.com/paper/1810.02894/) (2018)
- [Quantifying Ignorance in Individual-Level Causal-Effect Estimates under Hidden Confounding](https://mlsanity.com/paper/2103.04850/) (2021)
- [RieszNet and ForestRiesz: Automatic Debiased Machine Learning with Neural Nets and Random Forests](https://mlsanity.com/paper/2110.03031/) (2021)
- [Bounds on the conditional and average treatment effect with unobserved confounding factors](https://mlsanity.com/paper/1808.09521/) (2018)
- [De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers](https://mlsanity.com/paper/1802.08667/) (2018)
- [Sense and Sensitivity Analysis: Simple Post-Hoc Analysis of Bias Due to Unobserved Confounding](https://mlsanity.com/paper/2003.01747/) (2020)
- [Flexible sensitivity analysis for observational studies without observable implications](https://mlsanity.com/paper/1809.00399/) (2018)
- [Sensitivity analysis via the proportion of unmeasured confounding](https://mlsanity.com/paper/1912.02793/) (2019)
- [Nonparametric Bounds and Sensitivity Analysis of Treatment Effects](https://mlsanity.com/paper/1503.01598/) (2015)
- [Semiparametric sensitivity analysis: unmeasured confounding in observational studies](https://mlsanity.com/paper/2104.08300/) (2021)
- [Identification of Treatment Effects under Conditional Partial Independence](https://mlsanity.com/paper/1707.09563/) (2017)

## Built on by (most cited first, 23 of 23)

- [Applied Causal Inference Powered by ML and AI](https://mlsanity.com/paper/2403.02467/) (2024)
- [B-Learner: Quasi-Oracle Bounds on Heterogeneous Causal Effects Under Hidden Confounding](https://mlsanity.com/paper/2304.10577/) (2023)
- [Robust Fitted-Q-Evaluation and Iteration under Sequentially Exogenous Unobserved Confounders](https://mlsanity.com/paper/2302.00662/) (2023)
- [Robust Design and Evaluation of Predictive Algorithms under Unobserved Confounding](https://mlsanity.com/paper/2212.09844/) (2022)
- [The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning](https://mlsanity.com/paper/2410.09600/) (2024)
- [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022)
- [Automatic Debiased Machine Learning for Smooth Functionals of Nonparametric M-Estimands](https://mlsanity.com/paper/2501.11868/) (2025)
- [Quantitative probing: Validating causal models using quantitative domain knowledge](https://mlsanity.com/paper/2209.03013/) (2022)
- [Estimating Wage Disparities Using Foundation Models](https://mlsanity.com/paper/2409.09894/) (2024)
- [Efficient and Sharp Off-Policy Evaluation in Robust Markov Decision Processes](https://mlsanity.com/paper/2404.00099/) (2024)
- [Multiply-Robust Causal Change Attribution](https://mlsanity.com/paper/2404.08839/) (2024)
- [Adventures in Demand Analysis Using AI](https://mlsanity.com/paper/2501.00382/) (2024)
- [Doctor Rashomon and the UNIVERSE of Madness: Variable Importance with Unobserved Confounding and the Rashomon Effect](https://mlsanity.com/paper/2510.12734/) (2025)
- [Distributionally Robust Causal Inference with Observational Data](https://mlsanity.com/paper/2210.08326/) (2022)
- [Isolated Causal Effects of Natural Language](https://mlsanity.com/paper/2410.14812/) (2024)
- [What if? Causal Machine Learning in Supply Chain Risk Management](https://mlsanity.com/paper/2408.13556/) (2024)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Omitted Variable Bias in Language Models Under Distribution Shift](https://mlsanity.com/paper/2602.16784/) (2026)
- [Segment Discovery: Enhancing E-commerce Targeting](https://mlsanity.com/paper/2409.13847/) (2024)
- [Latent Variable Modeling for Robust Causal Effect Estimation](https://mlsanity.com/paper/2508.20259/) (2025)
- [Guardrailed Uplift Targeting: A Causal Optimization Playbook for Marketing Strategy](https://mlsanity.com/paper/2512.19805/) (2025)
- [Automatic debiased machine learning and sensitivity analysis for sample selection models](https://mlsanity.com/paper/2601.08643/) (2026)
- [Embedding-Bias in Conditional Independence Testing](https://mlsanity.com/paper/2610.11584/) (2026)

## Abstract (arXiv)

We develop a general theory of omitted variable bias for a wide range of common causal parameters, including (but not limited to) averages of potential outcomes, average treatment effects, average causal derivatives, and policy effects from covariate shifts. Our theory applies to nonparametric models, while naturally allowing for (semi-)parametric restrictions (such as partial linearity) when such assumptions are made. We show how simple plausibility judgments on the maximum explanatory power of omitted variables are sufficient to bound the magnitude of the bias, thus facilitating sensitivity analysis in otherwise complex, nonlinear models. Finally, we provide flexible and efficient statistical inference methods for the bounds, which can leverage modern machine learning algorithms for estimation. These results allow empirical researchers to perform sensitivity analyses in a flexible class of machine-learned causal models using very simple, and interpretable, tools. We demonstrate the utility of our approach with two empirical examples.