arXiv 12 Apr 2026 · Econometrics
arXiv:2604.10770 · PDF · DOI · OpenAlex · Extracted main text
Empirical researchers increasingly use upstream machine-learning (ML) methods to construct proxies for latent target variables from complex, unstructured data. A naive plug-in use of such proxies in downstream econometric models, however, can lead to biased estimation and invalid inference. This paper develops a framework for partial identification and inference in general moment models with ML-generated proxies. Our approach does not require restrictive assumptions on the upstream ML procedure, such as consistency or known convergence rates, nor does it require a complete validation sample containing all variables used in the downstream analysis. Instead, we assume access to two datasets: a downstream sample containing observed covariates and the proxy, and an auxiliary validation sample containing joint observations on the proxy and its target variable. We treat the proxy as a linking variable between these two samples, rather than as a literal noisy substitute for the latent target variable. Building on this idea, we develop a sharp identification strategy based on an unconditional optimal transport characterization and an inference procedure that controls asymptotic size using analytical critical values without resampling. Monte Carlo simulations show reliable size control and informative confidence sets across a range of predictive-accuracy scenarios.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Villani, Cédric (2009) Optimal Transport: Old and New | 0.928 | 4 | 3 | 100% |
| 2 | Fan, Yanqin and Park, Hyeonseok and Pass, Brendan and Shi, Xuetao (2025) Partial Identification in Moment Models with Incomplete Data–A Conditional Optimal Transport Approach | 0.874 | 6 | 2 | 100% |
| 3 | Sager, Lutz and Singer, Gregor (2025) Clean Identification? The Effects of the Clean Air Act on Air Pollution, Exposure Disparities, and House Prices | 0.874 | 5 | 2 | 100% |
| 4 | Groseclose, T. and Milyo, J (2005) A Measure of Media Bias | 0.811 | 4 | 2 | 100% |
| 5 | Gentzkow, Matthew and Shapiro, Jesse (2010) What Drives Media Slant? Evidence From U.S. Daily Newspapers | 0.737 | 3 | 2 | 100% |
| 6 | Battaglia, Laura and Christensen, Timothy and Hansen, Stephen and Sa… (2025) Inference for Regression with Variables Generated by AI or Machine Learning | 0.644 | 2 | 2 | 100% |
| 7 | Cross, Philip J. and Manski, Charles F (2002) Regressions, Short and Long | 0.644 | 2 | 2 | 100% |
| 8 | D’Haultfœuille, X and Gaillac, C and Maurel, A (2025) Partially Linear Models under Data Combination | 0.644 | 2 | 2 | 100% |
| 9 | Hansen, Stephen and Lambert, Peter John and Bloom, Nick and Davis, S… (2023) Remote Work across Jobs, Companies, and Space | 0.644 | 2 | 2 | 100% |
| 10 | Hwang, Yujung (2025) Bounding Omitted Variable Bias Using Auxiliary Data: With an Application to Estimate Neighborhood Effects | 0.644 | 2 | 2 | 100% |
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