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Inference for Regression with Variables Generated by AI or Machine Learning

Laura Battaglia, Timothy Christensen, Stephen Hansen, Szymon Sacher

arXiv 23 Feb 2024 · Econometrics · 2 citations (OpenAlex)

arXiv:2402.15585 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

83
references
133
in-text mentions
83
distinct cited
5
self-citations
17,742
main-text words

appendix boundary found by appendix_command · 56% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Baker, S. R., Bloom, N., and Davis, S. J (2016) Measuring Economic Policy Uncertainty1.00073100%
2Bandiera, O., Prat, A., Hansen, S., and Sadun, R (2020) CEO Behavior and Firm Performance self1.00053100%
3Gorodnichenko, Y., Pham, T., and Talavera, O (2023) The Voice of Monetary Policy0.87492100%
4Hansen, S., Lambert, P. J., Bloom, N., Davis, S. J., Sadun, R., and… (2023) Remote Work across Jobs, Companies, and Space self0.81142100%
5Bing, X., Bunea, F., and Wegkamp, M (2020) Optimal estimation of sparse topic models0.7374350%
6Ke, Z. T. and Wang, M (2022) Using SVD for Topic Modeling0.7374350%
7Wu, R., Zhang, L., and Tony Cai, T (2023) Sparse Topic Modeling: Computational Efficiency, Near-Optimal Algorithms, and Statistical Inference0.7374350%
8Gürkaynak, R. S., Sack, B., and Swanson, E (2005) Do actions speak louder than words? The response of asset prices to monetary policy actions and statements0.73732100%
9Allon, G., Chen, D., Jiang, Z., and Zhang, D (2023) Machine Learning and Prediction Errors in Causal Inference0.64422100%
10Ash, E., Morelli, M., and Vannoni, M (2025) More Laws, More Growth? Evidence from U.S. States0.64422100%

Showing the top 10 of 83 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Bootstrapping with AI/ML-generated labels1.000346
2Econometric Inference with Machine-Learned Proxies: Partial Identification via Data Combination0.64422
3Econometrics with Pre-Trained Embeddings for Unstructured Data0.51121
4Large Language Models: An Applied Econometric Framework0.40511
5Empirical Bayes shrinkage (mostly) does not correct the measurement error in regression0.40511
6A Unifying Framework for Robust and Efficient Inference with Unstructured Data0.40511
7Making Interpretable Discoveries from Unstructured Data: A High-Dimensional Multiple Hypothesis Testing Approach0.40511
8From Unstructured Data to Demand Counterfactuals: Theory and Practice0.40511
9Moment-Based Inference for Regression with Latent Dirichlet Covariates0.40511
10AI-Assisted Variance Reduction in Randomized Experiments0.40511