Bootstrapping with AI/ML-generated labels

TL;DR

This paper examines bootstrap methods to correct biases in regression analyses caused by AI/ML-generated labels, proposing a new coupled-label bootstrap that ensures valid inference.

Contribution

It introduces a coupled-label bootstrap approach that remains valid without strong independence assumptions, improving inference accuracy in models with ML-generated labels.

Findings

The fixed-label bootstrap is generally invalid unless a strong independence condition holds.

The coupled-label bootstrap is valid without the independence condition.

Finite-sample adjustments enhance coverage and inference reliability.

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.