We develop an empirical Bayes (EB) G-modeling framework for short-panel linear models with multidimensional heterogeneity and nonparametric prior. Specifically, we allow heterogeneous intercepts, slopes, dynamics, and a non-spherical error covariance structure. 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 resulting 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.

翻译：本文针对具有多维异质性和非参数先验的短面板线性模型，提出了一个经验贝叶斯（EB）G-建模框架。具体而言，我们允许异质性截距、斜率、动态性以及非球形误差协方差结构。我们在一般条件下建立了非参数极大似然估计量（NPMLE）的可识别性与一致性，并为若干实证研究关注的模型提供了低阶充分条件。同时，我们也确立了所得EB估计量的遗憾一致性条件。NPMLE的计算采用适用于面板回归的Wasserstein-Fisher-Rao梯度流算法。基于收入动态面板研究数据，我们发现潜在经验变量的斜率系数存在显著异质性，且与随机截距呈负相关；误差方差与自回归系数在个体间也存在显著差异。相较于个体极大似然估计，EB估计有效降低了均方预测误差。