Structural VAR and the VECM

A reduced-form VAR can forecast the joint movement of yields, inflation, and returns, but it cannot by itself say which innovation is a monetary-policy shock rather than a simultaneous reaction to news. A structural VAR (SVAR) makes that leap only by imposing economically defended restrictions. At the same time, a VAR in differences misses the equilibrium relation when the level variables are cointegrated. The vector error-correction model (VECM) restores that relation. This note puts those two qualifications beside the usual VAR toolkit: one identifies shocks; the other preserves long-run information.

• distinguish reduced-form innovations from structural shocks;
• state why an SVAR requires short-run, long-run, or other identifying restrictions;
• write the VECM representation of a cointegrated VAR;
• interpret $\boldsymbol\Pi=\boldsymbol\alpha\boldsymbol\beta'$ as adjustment loadings times cointegrating vectors;
• choose between a level VAR, a differenced VAR, and a VECM after integration-order and rank analysis.

1. From reduced form to structural shocks
2. Cointegration changes the VAR parameterisation
3. Rank before restriction