Empirical Bayes Estimation in Heterogeneous Coefficient Panel Models

TL;DR

This paper introduces an empirical Bayes framework for panel models with nonparametric priors, establishing theoretical properties and demonstrating improved prediction accuracy using real data.

Contribution

It develops a novel EB G-modeling approach with theoretical guarantees and applies it to real-world panel data, revealing significant heterogeneity and improved predictions.

Findings

Significant heterogeneity in slope coefficients for experience.

Error variances and autoregressive coefficients vary across individuals.

EB estimates outperform individual MLE in prediction errors.

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.