# Bootstrapping with AI/ML-generated labels

arXiv: https://arxiv.org/abs/2604.23770 · HTML: https://mlsanity.com/paper/2604.23770/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 26 Apr 2026.

## Builds on (most cited first, 6 of 6)

- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Large Language Models: An Applied Econometric Framework](https://mlsanity.com/paper/2412.07031/) (2024)
- [Inference for Regression with Variables Generated by AI or Machine Learning](https://mlsanity.com/paper/2402.15585/) (2024)
- [A Unifying Framework for Robust and Efficient Inference with Unstructured Data](https://mlsanity.com/paper/2505.00282/) (2025)
- [Simple Estimation of Semiparametric Models with Measurement Errors](https://mlsanity.com/paper/2306.14311/) (2023)

## Abstract (arXiv)

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.