flat

VAR with Flat Prior (Flat)

Description

VAR estimation with flat (uninformative) prior that provides minimal prior restrictions on coefficients. Equivalent to a Minnesota prior with very large λ₁ (> 999), effectively making the prior diffuse.

Technical Details

• Implements prior = 41 in BEAR5 terminology
• Uses Minnesota prior structure but with λ₁ > 999 to make priors uninformative
• Provides Bayesian estimation with minimal prior influence
• Useful when prior information is limited or when data should drive results

User Settings (Hyperparameters)

Inherited Base Settings

Burnin (double)

• Description: Number of burn-in draws for posterior sampling
• Default: 0
• Details: Number of initial MCMC draws to discard before collecting posterior samples

StabilityThreshold (double)

• Description: Threshold for maximum eigenvalue magnitude to ensure VAR stability
• Default: Inf (no stability check)
• Details: Maximum allowed eigenvalue magnitude; draws with eigenvalues exceeding this are rejected

MaxNumUnstableAttempts (double)

• Description: Maximum number of unstable sampling attempts before giving up
• Default: 1000
• Details: If stability checking is enabled, this limits the number of consecutive unstable draws before termination

Flat-Specific Settings

BlockExogenous (logical)

• Description: Block exogeneity restriction flag
• Default: false
• Details: Accessed by implementation but block exogeneity logic not implemented in current Flat algorithm

Implementation Notes

• Implements its own Gibbs sampling algorithm with diffuse (flat) priors directly
• Does not use the Minnesota prior framework or lambda parameters
• Uses Natural Conjugate (Normal-Inverse-Wishart) priors with diffuse parameterization
• Alternates between sampling VAR coefficients β and error covariance Σ
• Accesses BlockExogenous setting but lambda parameters are ignored
• Posterior results are dominated by the likelihood (data)

Usage Recommendations

• Limited prior information: Use when you have minimal prior beliefs about coefficients
• Data-driven analysis: When you want results to be primarily determined by the data
• Benchmark comparisons: Compare against informative priors to assess prior sensitivity
• Large sample sizes: Most effective when sample size is sufficient for stable estimation
• Model exploration: Useful for initial model exploration before imposing informative priors

Comparison to Other Estimators

• vs. Ordinary: Provides Bayesian uncertainty quantification vs. classical inference
• vs. Minnesota: Removes informative shrinkage toward random walk
• vs. Normal-Diffuse: Similar philosophy but different technical implementation ???

Limitations

• May lead to unstable estimates in small samples without prior regularization
• Less efficient than informative priors when prior beliefs are reasonable
• Can produce overfitting in large VAR models without sufficient data