-
Notifications
You must be signed in to change notification settings - Fork 1
dynamic_cross_panel
The Dynamic Cross-Unit Panel VAR extends the static cross-unit framework to allow for time-varying cross-unit dependencies through dynamic factor structures. This estimator models spillover effects between units that can evolve over time, incorporating both unit-specific dynamics and time-varying cross-unit relationships through common factors and stochastic volatility components.
The Dynamic Cross-Unit Panel VAR specification features:
- Unit-specific VAR dynamics with time-varying cross-unit dependencies
- Dynamic factor structure capturing evolving spillovers
- Stochastic volatility components for both factors and residuals
- Minnesota-type priors on within-unit coefficients
- Most flexible cross-unit panel VAR specification
This approach provides maximum flexibility in modeling cross-unit relationships by allowing spillover effects to vary over time through dynamic factor processes.
-
A0: IG shape parameter on factor variance
- Range: (0, ∞)
- Default: 1000
- Controls prior beliefs about factor variance distribution shape
-
B0: IG scale parameter on factor variance
- Range: (0, ∞)
- Default: 1
- Controls prior beliefs about factor variance level
-
Rho: AR coefficient on factors
- Range: [0, 1)
- Default: 0.75
- Controls persistence in common factor dynamics
-
Gamma: AR coefficient on residual variance
- Range: [0, 1)
- Default: 0.85
- Controls persistence in stochastic volatility process
-
Alpha0: IG shape parameter on residual variance
- Range: (0, ∞)
- Default: 1000
- Controls prior beliefs about residual variance distribution shape
-
Delta0: IG scale parameter on residual variance
- Range: (0, ∞)
- Default: 1
- Controls prior beliefs about residual variance level
-
Autoregression: Prior on first-order autoregression
- Range: [0, 1]
- Default: 0.8
- Controls the belief in random walk behavior for own lags
-
Lambda1: Overall tightness of priors
- Range: (0, ∞)
- Default: 0.1
- Smaller values impose tighter priors (more shrinkage)
-
Lambda2: Variable weighting
- Range: (0, ∞)
- Default: 0.5
- Controls relative weights between own-variable and cross-variable lags
-
Lambda3: Lag decay
- Range: (0, ∞)
- Default: 1
- Controls how quickly prior importance decays with lag length
-
Lambda4: Exogenous variable tightness
- Range: (0, ∞)
- Default: 100
- Controls prior tightness on exogenous variable coefficients
-
Lambda5: Block exogeneity shrinkage
- Range: (0, ∞)
- Default: 0.001
- Controls shrinkage when block exogeneity is imposed
-
Exogenous: Priors on exogenous variables flag
- Default: false
- Enables specialized priors for exogenous variables
-
BlockExogenous: Block exogeneity flag
- Default: false
- Imposes block exogeneity restrictions
-
Burnin: Number of burn-in draws
- Range: [0, ∞)
- Default: 0
- Recommended: Extensive burn-in due to complex dynamics
-
StabilityThreshold: Threshold for maximum eigenvalue magnitude
- Range: (0, ∞)
- Default: null (no stability check)
- Ensures stability of full dynamic system
-
MaxNumUnstableAttempts: Maximum number of unstable sampling attempts
- Range: [1, ∞)
- Default: 1000
- Maximum attempts to find stable draw before stopping
- Time-varying spillovers: When cross-unit relationships evolve over time
- Complex interdependencies: When spillover effects have rich dynamic structure
- Factor-driven spillovers: When cross-unit dependencies operate through common factors
- Evolving networks: When network relationships change over time
- Constant spillovers: When spillover effects are stable over time (use Static Cross Panel)
- Independent units: When units do not significantly affect each other
- Computational constraints: Extremely demanding computationally
- Short panels: When insufficient data for complex dynamic identification
- Requires very long time series for reliable parameter identification
- Extremely computationally intensive among panel VAR specifications
- Monitor convergence across factor, volatility, and spillover parameters
- Consider whether dynamic complexity provides meaningful improvements
For unit i:
y_{i,t} = Λᵢ f_t + Aᵢ y_{i,t-1} + ε_{i,t}
where f_t represents time-varying common factors.
Common factors follow AR processes:
f_t = ρ f_{t-1} + η_t
where η_t ~ N(0, Σ_f,t) with stochastic volatility.
Spillover effects operate through factor loadings Λᵢ and factor dynamics:
Spillover_{i→j,t} = Λⱼ × f_t × (effect of unit i on f_t)
Both factor and residual variances follow SV processes:
log(σ²_f,t) = γ_f log(σ²_f,t-1) + ζ_f,t
log(σ²_ε,t) = γ_ε log(σ²_ε,t-1) + ζ_ε,t
- Speed: Extremely slow due to multiple stochastic processes
- Memory: Very high memory requirements for dynamic parameters
- Convergence: Complex convergence requiring specialized monitoring
- Scalability: Limited scalability with panel size and time dimension
- Joint estimation of factors, loadings, and volatilities
- Time-varying parameter space increases rapidly
- Multiple sources of parameter interactions
- Requires advanced MCMC algorithms
- Factor contributions: How common factors drive spillovers
- Loading evolution: How unit sensitivities to factors change
- Spillover persistence: Dynamic properties of cross-unit effects
- Volatility spillovers: How uncertainty transmits across units
- Common shocks: Global factors affecting all units
- Idiosyncratic shocks: Unit-specific innovations
- Spillover channels: Factor loadings as transmission mechanisms
- Dynamic networks: Evolving cross-unit relationships
- Time variation: Dynamic vs. constant spillovers
- Flexibility: Maximum flexibility vs. structured simplicity
- Computation: Much more demanding vs. already complex
- Applications: Complex evolving systems vs. stable relationships
- Panel structure: Cross-unit focus vs. variable-focused factors
- Dynamics: Panel-specific dynamics vs. general factor dynamics
- Spillovers: Explicit cross-unit modeling vs. factor summarization
- Complexity: Panel-specific complexity vs. factor complexity
- Start with static cross-unit models
- Add factor structure incrementally
- Introduce stochastic volatility last
- Use extensive initialization strategies
- Use state-of-the-art MCMC algorithms
- Plan for multi-day estimation runs
- Consider cloud computing resources
- Implement extensive convergence monitoring
- Validate factor evolution against economic events
- Assess spillover timing and magnitudes
- Compare volatility evolution with known crisis periods
- Evaluate dynamic forecasting performance
- Factor interpretability in economic terms
- Spillover patterns consistent with theory
- Volatility evolution matching historical patterns
- Cross-unit relationships aligned with institutional knowledge
- International financial market contagion with evolving transmission
- Regional business cycle synchronization analysis
- Supply chain disruption propagation with changing networks
- Climate shock transmission with evolving vulnerability
- Dynamic network analysis in economics
- Time-varying spillover measurement
- Crisis transmission mechanism studies
- Policy effectiveness across evolving systems
- Diebold, F.X. and K. Yilmaz (2014). "On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms"
- Canova, F. and M. Ciccarelli (2013). "Panel Vector Autoregressive Models: A Survey"
- Koop, G., M.H. Pesaran, and S.M. Potter (1996). "Impulse Response Analysis in Nonlinear Multivariate Models"
- Barigozzi, M. and M. Brownlees (2019). "NETS: Network Estimation for Time Series"