EconBase
← All papers

Empirical Bayes Estimation in Heterogeneous Coefficient Panel Models

Myunghyun Song, Sokbae Lee, Serena Ng

arXiv 11 Jan 2026 · Econometrics

arXiv:2601.07059 · PDF · DOI · OpenAlex · Extracted main text

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.

Citation extraction

41
references
60
in-text mentions
41
distinct cited
0
self-citations
15,968
main-text words

appendix boundary found by appendix_command · 57% 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
1Gu and Koenker (2017) Unobserved Heterogeneity in Income Dynamics: An Empirical Bayes Perspective1.00053100%
2Kiefer and Wolfowitz (1956) Consistency of the Maximum Likelihood Estimator in the Presence of Infinitely Many Incidental Parameters0.8434375%
3Yan, Wang, and Rigollet (2024) Learning Gaussian mixtures using the Wasserstein–Fisher–Rao gradient flow0.73732100%
4Adusumilli, Gu, and Tao (2025) Empirical Bayes for Compound Adaptive Experiments0.64422100%
5Walters (2024) Chapter 3 - Empirical Bayes methods in labor economics0.64422100%
6Robbins (1956) An Empirical Bayes Approach to Statistics0.64422100%
7Shen and Wu (2025) Poisson Empirical Bayes estimation: When does $g$-modeling beat $f$-modeling in theory (and in practice)?0.64422100%
8Bruni and Koch (1985) Identifiability of continuous mixtures of unknown Gaussian distributions0.6066233%
9Zhang, Cui, Sen, and Toh (2024) On Efficient and Scalable Computation of the Nonparametric Maximum Likelihood Estimator in Mixture Models0.51121100%
10Armstrong, Kolesár, and Plagborg-Møller (2022) Robust Empirical Bayes Confidence Intervals0.40511100%

Showing the top 10 of 41 scored citations.