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hierarchical_panel
Jaromír Beneš edited this page Mar 20, 2026
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Hierarchical Bayesian panel VAR that allows for heterogeneity across units while sharing information through a hierarchical prior structure. Each unit has its own VAR parameters, but these are drawn from a common distribution whose hyperparameters are themselves estimated.
- Each unit i has its own coefficient vector βᵢ and error covariance matrix Σᵢ
- Unit-specific coefficients are drawn from a common distribution: βᵢ ~ N(b, λ₁Ω_b)
- Hyperparameters (b, λ₁) are estimated from the data
- Information sharing occurs through the hierarchical prior structure
- Suitable for panels where units are heterogeneous but share common characteristics
- Description: Inverse-Gamma shape parameter for overall tightness hyperparameter λ₁
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Default:
0.001 - Details: Shape parameter for the IG prior on λ₁. Small values provide diffuse prior on the common variance across units ?
- Description: Inverse-Gamma scale parameter for overall tightness hyperparameter λ₁
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Default:
0.001 - Details: Scale parameter for the IG prior on λ₁. Together with S0, controls the prior distribution of cross-unit heterogeneity ?
- Description: Number of burn-in draws for posterior sampling
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Default:
0 - Details: Number of initial MCMC draws to discard before collecting posterior samples
- Description: Threshold for maximum eigenvalue magnitude to ensure VAR stability
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Default:
Inf(no stability check) - Details: Maximum allowed eigenvalue magnitude; draws with eigenvalues exceeding this are rejected ?
- Description: Maximum number of unstable sampling attempts before giving up
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Default:
1000 - Details: If stability checking is enabled, this limits the number of consecutive unstable draws before termination ?
- Description: Cross-variable weighting parameter for unit-specific priors
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Default:
0.5 - Details: Controls the relative tightness of priors on cross-variable coefficients vs. own-lag coefficients within each unit
- Description: Lag decay parameter for unit-specific priors
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Default:
1.0 - Details: Controls the rate of decay of prior variance with lag length within each unit. Higher values = faster decay
- Description: Exogenous variable tightness parameter for unit-specific priors
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Default:
100 - Details: Controls the tightness of priors on exogenous variables and constants within each unit. Higher values = looser priors
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Three-level hierarchy:
- Data level: yᵢₜ = Xᵢₜβᵢ + εᵢₜ, εᵢₜ ~ N(0, Σᵢ)
- Unit level: βᵢ ~ N(b, λ₁Ω_b), Σᵢ ~ IW(S̃ᵢ, T)
- Hyperparameter level: b ~ N(β̄, (1/N)λ₁Ω_b), λ₁ ~ IG(s₀, v₀)
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Sampling sequence:
- Draw common mean b from its conditional posterior
- Draw variance hyperparameter λ₁ from its conditional posterior
- Draw unit-specific parameters (βᵢ, Σᵢ) for each unit
- Prior structure: Unit-specific priors Ω_b follow Minnesota-style structure with λ₂, λ₃, λ₄ parameters
- Cross-unit heterogeneity: Increase S0 and V0 for more diffuse priors on λ₁, allowing more heterogeneity ?
- Strong pooling: Use smaller values of S0 and V0 to encourage more similar parameters across units ?
- Standard panel applications: Use default hierarchical hyperparameters (S0=V0=0.001)
- Unit-specific priors: Adjust λ₂, λ₃, λ₄ similar to Minnesota VAR guidelines
- Sample size considerations: Requires sufficient observations per unit for stable estimation
- Cannot be used with dummy observations (CanHaveDummies = false)
- Requires balanced panel data with sufficient time series length per unit ?
- Computational intensity scales with number of units
- Assumes common prior structure across all units (may be restrictive)
- vs. MeanOLSPanel: More flexible, allows for unit-specific error covariances
- vs. NormalWishartPanel: Hierarchical structure provides automatic determination of pooling degree
- vs. Cross-unit panels: No cross-unit spillovers, units are separable