Empirical Bayes vs Hierarchical Bayes

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For a hierarchical model y_{i} ∣ θ_{i} \sim p (\cdot ∣ θ_{i}), θ_{i} ∣ ψ \sim π (\cdot ∣ ψ), the empirical Bayes (EB) and full hierarchical Bayes (HB) approaches differ in how they treat ψ . What is the primary statistical consequence?