Empirical Bayes Estimation in Heterogeneous Coefficient Panel Models

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.

💡 Research Summary

The paper introduces a comprehensive empirical Bayes (EB) framework for short‑panel linear models that allows heterogeneity in four dimensions: individual intercepts, slopes, dynamic (autoregressive) coefficients, and error variances. The authors call the most general specification the HIVDX model and embed it within a broader heterogeneous‑coefficient (HC) formulation. Under the assumption that the vector of individual‑specific parameters θ_i = (a_i, b_i, ρ_i, σ_i^2) is an i.i.d. draw from an unknown prior distribution G*, the optimal compound decision rule is the posterior mean θ_i* = E_G*