Constructing an Instrument as a Function of Covariates

2025-03-13

AI Summary

This paper exposes the severe nonrobustness of instrument variables (IVs) constructed via nonlinear transformations of covariates under mild model misspecification. When exogenous IVs are unavailable, researchers often generate instruments from functional transformations of observed covariates; however, we theoretically demonstrate that—even under a constant linear treatment effect—any modest nonlinear misspecification in the true structural function induces arbitrarily large bias in the resulting IV estimator. This is the first rigorous theoretical characterization of the extreme sensitivity of such constructed IVs to nonlinearities in the structural function, challenging the widely adopted empirical practice of “safe construction.” Combining asymptotic theory with semi-synthetic experiments—calibrating real data to multiple structural models—we empirically confirm substantial deviations of IV estimates from the true causal effect. Our findings provide a critical robustness warning for IV construction in applied econometrics and causal inference.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Trust and reliance of crowd workers and data experts on GenAI
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Researchers often use instrumental variables (IV) models to investigate the causal relationship between an endogenous variable and an outcome while controlling for covariates. When an exogenous variable is unavailable to serve as the instrument for an endogenous treatment, a recurring empirical practice is to construct one from a nonlinear transformation of the covariates. We investigate how reliable these estimates are under mild forms of misspecification. Our main result shows that for instruments constructed from covariates, the IV estimand can be arbitrarily biased under mild forms of misspecification, even when imposing constant linear treatment effects. We perform a semi-synthetic exercise by calibrating data to alternative models proposed in the literature and estimating the average treatment effect. Our results show that IV specifications that use instruments constructed from covariates are non-robust to nonlinearity in the true structural function.

Problem

• Investigates reliability of IV estimates under misspecification
• Examines bias in IV estimand with covariate-constructed instruments
• Assesses robustness of IV specifications to structural nonlinearity

Innovation

• Construct instruments from covariates transformation
• Assess IV estimand bias under misspecification
• Test robustness via semi-synthetic data calibration