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Empirical Bayes Estimation in Heterogeneous Coefficient Panel Models

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  • Myunghyun Song
  • Sokbae Lee
  • Serena Ng

Abstract

We develop an empirical Bayes (EB) G-modeling framework for short-panel linear models with nonparametric prior for the random intercepts, slopes, dynamics, and non-spherical error variances. We establish identification and consistency of the nonparametric maximum likelihood estimator (NPMLE) under general conditions, and provide low-level sufficient conditions for several models of empirical interest. Conditions for regret consistency of the EB estimators are also established. The NPMLE is computed using a Wasserstein-Fisher-Rao gradient flow algorithm adapted to panel regressions. Using data from the Panel Study of Income Dynamics, we find that the slope coefficient for potential experience is substantially heterogeneous and negatively correlated with the random intercept, and that error variances and autoregressive coefficients vary significantly across individuals. The EB estimates reduce mean squared prediction errors relative to individual maximum likelihood estimates.

Suggested Citation

  • Myunghyun Song & Sokbae Lee & Serena Ng, 2026. "Empirical Bayes Estimation in Heterogeneous Coefficient Panel Models," Papers 2601.07059, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2601.07059
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    References listed on IDEAS

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    1. Timothy B. Armstrong & Michal Kolesár & Mikkel Plagborg‐Møller, 2022. "Robust Empirical Bayes Confidence Intervals," Econometrica, Econometric Society, vol. 90(6), pages 2567-2602, November.
    2. Timothy B. Armstrong & Michal Koles'ar & Mikkel Plagborg-M{o}ller, 2020. "Robust Empirical Bayes Confidence Intervals," Papers 2004.03448, arXiv.org, revised May 2022.
    3. Joseph Altonji & Disa Hynsjo & Ivan Vidangos, 2023. "Individual Earnings and Family Income: Dynamics and Distribution," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 49, pages 225-250, July.
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