A structural VAR identified by a recursive (Cholesky) ordering produces orthogonalized impulse-response functions and a forecast-error variance decomposition, with optional bootstrap bands.
A reduced-form VAR captures the dynamics of the system but its residuals are correlated, so a shock to one equation can't be interpreted in isolation. Identification imposes structure on how the reduced-form errors map to uncorrelated structural shocks. The recursive scheme (Sims 1980) factors the residual covariance as Σ = P·P′ with P lower-triangular (the Cholesky factor): the variable ordered first responds only to its own shock contemporaneously, the second to the first two, and so on.
Orthogonalized impulse responses Θ_h = Φ_h·P trace each variable's reaction over h periods to a one-standard-deviation structural shock, where Φ_h are the VAR's moving-average coefficients. The forecast-error variance decomposition (FEVD) splits each variable's h-step forecast-error variance into the share attributable to each structural shock.
≥ 2 numeric series (row order = time) + lag order p + horizon + deterministic terms + an optional Cholesky ordering.
The lower-triangular impact matrix P, orthogonalized impulse responses (optionally with a bootstrap band), and the forecast-error variance decomposition at each horizon.
The variable ordering is an identifying assumption, not an estimate: reorder the series and the short-horizon responses change. Later-ordered variables cannot affect earlier ones on impact.
FEVD shares for a variable sum to 100% at every horizon.