Impulse Response Function (IRF)

The ordering implies a recursive causal structure: a variable placed first is assumed not to respond contemporaneously to any other variable in the system. The ordering should be grounded in economic theory or institutional timing (e.g., central bank decisions lagging market signals). Robustness checks across alternative orderings are strongly recommended; if results change materially, consider structural identification via sign restrictions instead.

Orthogonalized IRFs use Cholesky decomposition to isolate shocks to one variable at a time, making them order-dependent. Generalized IRFs, introduced by Pesaran and Shin (1998), do not require orthogonalization and are invariant to variable ordering, but they do not have a structural interpretation. For policy analysis requiring shock isolation, orthogonalized or SVAR-based IRFs are preferred; for reduced-form forecasting contexts, generalized IRFs offer a convenient order-invariant summary.

The horizon h should be long enough to capture the full dynamic adjustment of the system back toward equilibrium. In quarterly macroeconomic models, 12 to 20 quarters is typical; in monthly financial data, 12 to 24 months. The IRF should visually return to zero (or a constant if the shock has permanent effects) before truncation. Always verify that the estimated VAR satisfies the stability condition — all eigenvalues of the companion matrix inside the unit circle — before interpreting long-horizon IRFs.