Individual Shrinkage for Random Effects

Abstract: This paper develops a novel approach to random effects estimation and individual-level forecasting in micropanels, targeting individual accuracy rather than aggregate performance. The conventional shrinkage methods used in the literature, such as the James-Stein estimator and Empirical Bayes, target aggregate performance and can lead to inaccurate decisions at the individual level. We propose a class of shrinkage estimators with individual weights (IW) that leverage an individual's own past history, instead of the cross-sectional dimension. This approach overcomes the "tyranny of the majority" inherent in existing methods, while relying on weaker assumptions. A key contribution is addressing the challenge of obtaining feasible weights from short time-series data and under parameter heterogeneity. We discuss the theoretical optimality of IW and recommend using feasible weights determined through a Minimax Regret analysis in practice.