Empirical Bayes shrinkage (mostly) does not correct the measurement error in regression
Econometrics
2026-02-23 v2 Methodology
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.
Keywords
Cite
@article{arxiv.2503.19095,
title = {Empirical Bayes shrinkage (mostly) does not correct the measurement error in regression},
author = {Jiafeng Chen and Jiaying Gu and Soonwoo Kwon},
journal= {arXiv preprint arXiv:2503.19095},
year = {2026}
}