# Strategic Instrumental Variable Regression: Recovering Causal Relationships From Strategic Responses

arXiv: https://arxiv.org/abs/2107.05762 · HTML: https://mlsanity.com/paper/2107.05762/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 52 references that are in the map.
- First posted on arXiv 12 Jul 2021.

## Builds on (most cited first, 22 of 22)

- [Counterfactual Fairness](https://mlsanity.com/paper/1703.06856/) (2017)
- [Performative Prediction](https://mlsanity.com/paper/2002.06673/) (2020)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [Causality for Machine Learning](https://mlsanity.com/paper/1911.10500/) (2019)
- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Outside the Echo Chamber: Optimizing the Performative Risk](https://mlsanity.com/paper/2102.08570/) (2021)
- [Discrimination in Online Ad Delivery](https://mlsanity.com/paper/1301.6822/) (2013)
- [Stochastic Optimization for Performative Prediction](https://mlsanity.com/paper/2006.06887/) (2020)
- [Strategic Classification is Causal Modeling in Disguise](https://mlsanity.com/paper/1910.10362/) (2019)
- [How Do Classifiers Induce Agents To Invest Effort Strategically?](https://mlsanity.com/paper/1807.05307/) (2018)
- [On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems](https://mlsanity.com/paper/2006.11144/) (2020)
- [The Disparate Effects of Strategic Manipulation](https://mlsanity.com/paper/1808.08646/) (2018)
- [Causal Strategic Linear Regression](https://mlsanity.com/paper/2002.10066/) (2020)
- [Causal Reasoning for Algorithmic Fairness](https://mlsanity.com/paper/1805.05859/) (2018)
- [On the Long-term Impact of Algorithmic Decision Policies: Effort Unfairness and Feature Segregation through Social Learning](https://mlsanity.com/paper/1903.01209/) (2019)
- [The Disparate Equilibria of Algorithmic Decision Making when Individuals Invest Rationally](https://mlsanity.com/paper/1910.04123/) (2019)
- [What does it mean to solve the problem of discrimination in hiring? Social, technical and legal perspectives from the UK on automated hiring systems](https://mlsanity.com/paper/1910.06144/) (2019)
- [From Fair Decision Making to Social Equality](https://mlsanity.com/paper/1812.02952/) (2018)
- [Stateful Strategic Regression](https://mlsanity.com/paper/2106.03827/) (2021)
- [Optimum Statistical Estimation with Strategic Data Sources](https://mlsanity.com/paper/1408.2539/) (2014)
- [Truthful Linear Regression](https://mlsanity.com/paper/1506.03489/) (2015)
- [Instrument-Armed Bandits](https://mlsanity.com/paper/1705.07377/) (2017)

## Built on by (most cited first, 30 of 32)

- [Anticipating Performativity by Predicting from Predictions](https://mlsanity.com/paper/2208.07331/) (2022)
- [The Sample Complexity of Online Contract Design](https://mlsanity.com/paper/2211.05732/) (2022)
- [Generalized Strategic Classification and the Case of Aligned Incentives](https://mlsanity.com/paper/2202.04357/) (2022)
- [Causal Strategic Classification: A Tale of Two Shifts](https://mlsanity.com/paper/2302.06280/) (2023)
- [Bayesian Persuasion for Algorithmic Recourse](https://mlsanity.com/paper/2112.06283/) (2021)
- [Performative Recommendation: Diversifying Content via Strategic Incentives](https://mlsanity.com/paper/2302.04336/) (2023)
- [Strategic Apple Tasting](https://mlsanity.com/paper/2306.06250/) (2023)
- [Causal Strategic Learning with Competitive Selection](https://mlsanity.com/paper/2308.16262/) (2023)
- [Automating Data Annotation under Strategic Human Agents: Risks and Potential Solutions](https://mlsanity.com/paper/2405.08027/) (2024)
- [Online Learning in a Creator Economy](https://mlsanity.com/paper/2305.11381/) (2023)
- [Learning under Imitative Strategic Behavior with Unforeseeable Outcomes](https://mlsanity.com/paper/2405.01797/) (2024)
- [Performative Validity of Recourse Explanations](https://mlsanity.com/paper/2506.15366/) (2025)
- [Stochastic Online Instrumental Variable Regression: Regrets for Endogeneity and Bandit Feedback](https://mlsanity.com/paper/2302.09357/) (2023)
- [Strategic Classification With Externalities](https://mlsanity.com/paper/2410.08032/) (2024)
- [Learning In Reverse Causal Strategic Environments With Ramifications on Two Sided Markets](https://mlsanity.com/paper/2404.13240/) (2024)
- [Learning Instrumental Variable from Data Fusion for Treatment Effect Estimation](https://mlsanity.com/paper/2208.10912/) (2022)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Strategic Linear Contextual Bandits](https://mlsanity.com/paper/2406.00551/) (2024)
- [Incentive-Aware Machine Learning; Robustness, Fairness, Improvement & Causality](https://mlsanity.com/paper/2505.05211/) (2025)
- [Strategyproof Decision-Making in Panel Data Settings and Beyond](https://mlsanity.com/paper/2211.14236/) (2022)
- [Discovering Optimal Scoring Mechanisms in Causal Strategic Prediction](https://mlsanity.com/paper/2302.06804/) (2023)
- [Microfoundation Inference for Strategic Prediction](https://mlsanity.com/paper/2411.08998/) (2024)
- [Explanation Design in Strategic Learning: Sufficient Explanations that Induce Non-harmful Responses](https://mlsanity.com/paper/2502.04058/) (2025)
- [COBRA: Contextual Bandit Algorithm for Ensuring Truthful Strategic Agents](https://mlsanity.com/paper/2505.23720/) (2025)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)
- [Learning Under Moral Hazard with Instrumental Regression and Generalized Method of Moments](https://mlsanity.com/paper/2405.20642/) (2024)
- [Estimating Misreporting in the Presence of Genuine Modification: A Causal Perspective](https://mlsanity.com/paper/2505.23954/) (2025)
- [The Sample Complexity of Online Strategic Decision Making with Information Asymmetry and Knowledge Transportability](https://mlsanity.com/paper/2506.09940/) (2025)
- [Algometrics: Forecasting Under Algorithmic Feedback](https://mlsanity.com/paper/2605.23978/) (2026)
- [Off-Policy Evaluation with Strategic Agents via Local Disclosure](https://mlsanity.com/paper/2606.07308/) (2026)

## Abstract (arXiv)

In settings where Machine Learning (ML) algorithms automate or inform consequential decisions about people, individual decision subjects are often incentivized to strategically modify their observable attributes to receive more favorable predictions. As a result, the distribution the assessment rule is trained on may differ from the one it operates on in deployment. While such distribution shifts, in general, can hinder accurate predictions, our work identifies a unique opportunity associated with shifts due to strategic responses: We show that we can use strategic responses effectively to recover causal relationships between the observable features and outcomes we wish to predict, even under the presence of unobserved confounding variables. Specifically, our work establishes a novel connection between strategic responses to ML models and instrumental variable (IV) regression by observing that the sequence of deployed models can be viewed as an instrument that affects agents' observable features but does not directly influence their outcomes. We show that our causal recovery method can be utilized to improve decision-making across several important criteria: individual fairness, agent outcomes, and predictive risk. In particular, we show that if decision subjects differ in their ability to modify non-causal attributes, any decision rule deviating from the causal coefficients can lead to (potentially unbounded) individual-level unfairness.