Timothy Christensen, Silvia Goncalves, Benoit Perron
arXiv 26 Apr 2026 · Econometrics
arXiv:2604.23770 · PDF · DOI · OpenAlex · Extracted main text
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.
appendix boundary found by appendix_command · 69% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Battaglia, L., T. Christensen, S. Hansen, and S. Sacher (2025) Inference for Regression with Variables Generated by AI or Machine Learning | 1.000 | 34 | 6 | 100% |
| 2 | Hansen, S., P. J. Lambert, N. Bloom, S. J. Davis, R. Sadun, and B. T… (2026) Remote Work across Jobs, Companies, and Space, Working Paper 31007, NBER | 0.737 | 3 | 2 | 100% |
| 3 | Bursztyn, L., T. Chaney, T. A. Hassan, and A. Rao (2024) The Immigrant Next Door | 0.511 | 2 | 1 | 100% |
| 4 | Dupas, P., A. Handlan, A. S. Modestino, M. Niederle, M. Seré, H. She… (2026) Gender Differences in Economics Seminars | 0.511 | 2 | 1 | 100% |
| 5 | Adams-Prassl, A., T. Waters, M. Balgova, and M. Qian (2023) Firm Concentration & Job Design: The Case of Schedule Flexible Work Arrangements, Tech | 0.405 | 1 | 1 | 100% |
| 6 | Aigner, D. J (1973) Regression with a Binary Independent Variable Subject to Errors of Observation | 0.405 | 1 | 1 | 100% |
| 7 | Angelopoulos, A. N., J. C. Duchi, and T. Zrnic (2023) b): PPI++: Efficient Prediction-Powered Inference | 0.405 | 1 | 1 | 100% |
| 8 | Angelopoulos, A. N., S. Bates, C. Fannjiang, M. I. Jordan, and T. Zr… (2023) a): Prediction-Powered Inference | 0.405 | 1 | 1 | 100% |
| 9 | Bound, J., C. Brown, G. J. Duncan, and W. L. Rodgers (1994) Evidence on the Validity of Cross-Sectional and Longitudinal Labor Market Data | 0.405 | 1 | 1 | 100% |
| 10 | Bound, J. and A. B. Krueger (1991) The Extent of Measurement Error in Longitudinal Earnings Data: Do Two Wrongs Make a Right? | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 29 scored citations.