Bootstrapping with AI/ML-generated labels

2026-04-26

AI Summary

This study addresses the severe bias and invalid inference that arise in ordinary least squares (OLS) regression when binary labels generated by AI/ML models are used as covariates, even under minimal misclassification. To correct this bias without requiring the strong assumption that true labels are independent of other covariates, the authors propose a “coupled label bootstrap” method that jointly resamples both observed and estimated labels. The approach incorporates two finite-sample refinements: a variance correction accounting for uncertainty in misclassification rates and a Hessian-based rotation. Simulation studies and an empirical application examining the effect of remote work on wages demonstrate that the proposed method substantially improves confidence interval coverage, yielding more reliable statistical inference.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: Humans versus LLMs for data annotation and labeling
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

AI/ML methods are increasingly used in economics to generate binary variables (or labels) via classification algorithms. When these generated variables are included as covariates in regressions, even small misclassification errors can induce large biases in OLS estimators and invalidate standard inference. We study whether the bootstrap can correct this bias and deliver valid inference. We first show that a seemingly natural fixed-label bootstrap, which generates data using estimated labels but relies on a corrupted version in estimation, is generally invalid unless a strong independence condition between the latent true labels and other covariates holds. We then propose a coupled-label bootstrap that jointly resamples the true and imputed labels, and show it is valid without this condition. Two finite-sample adjustments further improve coverage: a variance correction for uncertainty in estimated misclassification rates and a Hessian rotation for near-singular designs. We illustrate the methods in simulations and apply them to investigate the relationship between wages and remote work status.

Problem

• misclassification bias
• bootstrap inference
• machine learning labels
• OLS estimation
• covariate error

Innovation

• coupled-label bootstrap
• misclassification bias
• variance correction
• Hessian rotation
• AI/ML-generated labels