minnesota_favar_twostep

Two-Step FAVAR with Minnesota Prior (MinnesotaFAVARTwostep)

Description

Factor-Augmented Vector Autoregression (FAVAR) using two-step estimation with Minnesota prior on VAR coefficients. Factors are first extracted via principal components, then used in a standard Minnesota VAR. Suitable for incorporating information from large datasets into VAR analysis.

Technical Details

• Two-step procedure:
  1. Extract factors from large dataset using principal component analysis
  2. Estimate VAR using factors and observed variables with Minnesota prior
• Factors summarize information from many variables (informational variables)
• Observed variables are directly included in the VAR
• Standard Minnesota prior applied to the factor-augmented VAR

User Settings (Hyperparameters)

FAVAR-Specific Settings

Note: FAVAR-specific settings (number of factors, factor datasets, etc.) are configured through the Meta and DataHolder components, not through estimator settings.

Minnesota Prior Settings (Inherited from Minnesota)

Sigma (string)

• Description: Method for calculating priors on error covariance matrix
• Default: "ar"
• Options:
  • "ar" (prior = 11): Use residual variances from univariate AR models
  • "diag" (prior = 12): Use diagonal elements of OLS VAR covariance matrix
  • "full" (prior = 13): Use full OLS VAR covariance matrix
• Details: Applied to the factor-augmented VAR system (factors + observed variables)

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

Minnesota Hyperparameters (Applied to Factor-Augmented System)

Lambda1 (double)

• Description: Overall tightness of the Minnesota prior
• Default: 0.1
• Details: Controls overall shrinkage intensity for all variables in the factor-augmented system (factors + observed variables). May need adjustment for FAVAR systems ???

Lambda2 (double)

• Description: Cross-variable weighting parameter
• Default: 0.5
• Details: Controls relative tightness of priors on cross-variable coefficients. Applied to interactions between factors, between observed variables, and between factors and observed variables

Lambda3 (double)

• Description: Lag decay parameter
• Default: 1.0
• Details: Controls rate of decay of prior variance with lag length. Applied uniformly across the factor-augmented system

Lambda4 (double matrix)

• Description: Exogenous variable tightness parameter
• Default: 100
• Details: Controls tightness of priors on exogenous variables and constants in the factor-augmented VAR

Lambda5 (double)

• Description: Block exogeneity shrinkage parameter
• Default: 0.001
• Details: Additional shrinkage factor for block exogeneity restrictions in the factor-augmented system ???

Autoregression (double vector)

• Description: Prior mean for first-order autoregressive coefficients
• Default: 0.8
• Details: Prior mean for coefficients on own first lags. Applied to both factors and observed variables

Block Structure Settings

Exogenous (logical matrix)

• Description: Flags for applying priors to exogenous variables
• Default: false
• Details: Controls whether to apply informative priors to exogenous variables in the factor-augmented system

BlockExogenous (logical)

• Description: Block exogeneity restriction flag
• Default: false
• Details: Imposes block exogeneity restrictions in the factor-augmented VAR (e.g., factors don't respond to observed variables within period) ???

FAVAR Implementation Notes

• Factor extraction: Factors are extracted from a large panel of informational variables using principal components
• Factor selection: Number of factors typically chosen using information criteria or cross-validation ?
• Identification: Factors are only identified up to rotation; economic interpretation requires careful analysis
• Minnesota prior application: Standard Minnesota shrinkage applied to the augmented system treating factors as additional variables

Usage Recommendations

Prior Tuning for FAVAR

• Lambda1: May need to be smaller than standard VAR applications due to larger system size ???
• Lambda2: Standard values (0.3-0.7) usually work well for factor-variable interactions
• Factor treatment: Factors often have similar prior treatment to observed variables, but may warrant different λ₂ weighting ???

FAVAR-Specific Considerations

• Sample size: Requires sufficient observations for both factor extraction and VAR estimation
• Factor interpretation: Factors may represent common economic forces but lack direct economic meaning
• Two-step uncertainty: Standard errors don't account for factor extraction uncertainty ???

Comparison to Other FAVAR Estimators

• vs. One-step FAVAR: Simpler computation but ignores factor extraction uncertainty
• vs. Other two-step priors: Minnesota provides good shrinkage for macro applications
• vs. Time-varying FAVAR: Constant parameters vs. time-varying relationships

Limitations

• Factor extraction uncertainty not accounted for in final inference ???
• Assumes factors are adequately represented by principal components
• Two-step procedure may be less efficient than joint estimation
• Requires specification of number of factors (model selection issue)

Technical Validation

• Check factor stability over time
• Verify adequate factor representation of informational variables
• Compare results with benchmark VAR using only observed variables
• Assess sensitivity to number of factors chosen