Inference for Regression with Variables Generated by AI or Machine Learning

Laura Battaglia, Timothy Christensen, Stephen Hansen and Szymon Sacher

Papers from arXiv.org

Abstract: Researchers now routinely use AI or other machine learning methods to estimate latent variables of economic interest, then plug-in the estimates as covariates in a regression. We show both theoretically and empirically that naively treating AI/ML-generated variables as "data" leads to biased estimates and invalid inference. To restore valid inference, we propose two methods: (1) an explicit bias correction with bias-corrected confidence intervals, and (2) joint estimation of the regression parameters and latent variables. We illustrate these ideas through applications involving label imputation, dimensionality reduction, and index construction via classification and aggregation.

Date: 2024-02, Revised 2025-04
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Working Paper: Inference for Regression with Variables Generated by AI or Machine Learning (2025)
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