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Empirical Bayes shrinkage (mostly) does not correct the measurement error in regression

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  • Jiafeng Chen
  • Jiaying Gu
  • Soonwoo Kwon

Abstract

In the value-added literature, it is often claimed that regressing on empirical Bayes shrinkage estimates corrects for the measurement error problem in linear regression. We clarify the conditions needed; we argue that these conditions are stronger than the those needed for classical measurement error correction, which we advocate for instead. Moreover, we show that the classical estimator cannot be improved without stronger assumptions. We extend these results to regressions on nonlinear transformations of the latent attribute and find generically slow minimax estimation rates.

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  • Jiafeng Chen & Jiaying Gu & Soonwoo Kwon, 2025. "Empirical Bayes shrinkage (mostly) does not correct the measurement error in regression," Papers 2503.19095, arXiv.org.
    • Handle: RePEc:arx:papers:2503.19095
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    File URL: http://arxiv.org/pdf/2503.19095
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    References listed on IDEAS

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    1. Victoria Angelova & Will S. Dobbie & Crystal Yang, 2023. "Algorithmic Recommendations and Human Discretion," NBER Working Papers 31747, National Bureau of Economic Research, Inc.
    2. Laura Battaglia & Timothy Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for Regression with Variables Generated by AI or Machine Learning," Papers 2402.15585, arXiv.org, revised Apr 2025.
    3. Laura Battaglia & Timothy M. Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for regression with variables generated from unstructured data," CeMMAP working papers 10/24, Institute for Fiscal Studies.
    4. Jean-Francois Mertens & Abraham Neyman, 2001. "A Value on 'AN," Discussion Paper Series dp276, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
      • MERTENS, Jean-François & NEYMAN, Abraham, 2003. "A value on 'AN," LIDAM Reprints CORE 1739, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Tian Xie, 2025. "Automatic Inference for Value-Added Regressions," Papers 2503.19178, arXiv.org.

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