Dynamic Models and Vector Autoregression
EVIDENCE LAB · 11
Dynamic Models
& Vector Autoregression.
Economic variables respond with delay and interact through feedback. Learn to model persistence, multivariate dynamics and the propagation of structural innovations.
LAGSSHOCKRESPONSE
01 · DYNAMIC BUILDING BLOCKS
Today depends
on yesterday.
Persistence
The variable depends on its own previous value. Stability requires |ρ| < 1.
Yₜ = α + ρYₜ₋₁ + εₜ
Distributed lag
An explanatory variable affects the outcome now and across later periods.
Yₜ = α + ΣβⱼXₜ₋ⱼ + εₜ
System feedback
Every variable may depend on lags of every variable in the system.
Yₜ = c + A₁Yₜ₋₁ + uₜ
02 · THE VAR SYSTEM
Endogenous variables
evolve together.
Lag selection
Too few lags omit dynamics; too many consume degrees of freedom and weaken precision.
Identification
Reduced-form innovations are correlated mixtures. Structural interpretation requires restrictions.
Impulse response
An IRF traces the time path of all variables after a one-time identified shock.
VAR DYNAMICS STUDIO
Shock the system.
Trace the response.
Select an innovation, its magnitude, persistence and cross-variable transmission. ECONORIA generates impulse responses for output, inflation and the policy rate.
Output response
Inflation response
Policy-rate response
SYSTEM INTERPRETATION
03 · VAR DISCIPLINE
Dynamic patterns are not structural truth
without identification.
Check stationarity
Model stable dynamics or justify cointegration and error correction.
Select lags
Use information criteria, diagnostics and economic timing.
Defend ordering
Recursive identification embeds contemporaneous assumptions.
Report uncertainty
Impulse responses require confidence bands and robustness checks.
