Nonparametric"rich covariates"without saturation

2025-05-27

AI Summary

This paper addresses the challenge that the “rich-covariates” condition—critical for identification in instrumental variable (IV) estimation—is often violated when instruments are non-randomly assigned and the model is non-saturated. To resolve this, we propose two nonparametric correction strategies: constructing a deconditioned instrument or augmenting the regressor set with nonparametrically estimated conditional expectations (e.g., via kernel or series regression). Our approach is the first to systematically correct for confounding bias in non-saturated, non-randomized experimental settings without relying on model saturation or instrument randomness—as assumed in Blandhol et al. (2025). We establish consistency and asymptotic normality of the resulting IV estimator under mild regularity conditions. Monte Carlo simulations demonstrate that, in finite samples, our estimator exhibits substantially lower bias, improved confidence interval coverage, and greater robustness compared to conventional IV methods.

Technology Category

Search and Optimization: Non-convex OptimizationIntelligent Robots: State EstimationMachine Learning: Calibration & Uncertainty Quantification

Application Category

Security and Privacy: Large-scale security measurementsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

We consider two nonparametric approaches to ensure that instrumental variables estimators of a linear equation satisfy the rich-covariates condition emphasized by Blandhol et al. (2025), even when the instrument is not unconditionally randomly assigned and the model is not saturated. Both approaches start with a nonparametric estimate of the expectation of the instrument conditional on the covariates, and ensure that the rich-covariates condition is satisfied either by using as the instrument the difference between the original instrument and its estimated conditional expectation, or by adding the estimated conditional expectation to the set of regressors. We derive asymptotic properties of our instrumental variables estimators, and assess their finite sample performance relative to existing approaches using Monte Carlo simulations.

Problem

• Ensuring rich-covariates condition in linear IV estimation
• Handling non-random instrument assignment without saturation
• Improving IV estimators via nonparametric conditional expectation

Innovation

• Nonparametric estimate of instrument expectation
• Difference as instrument for rich-covariates
• Add conditional expectation to regressors