What an impulse response can claim

The economic question

Reduced-form covariance does not uniquely determine economic shocks. A covariance-preserving rotation changes the impact pattern while retaining observable second moments.

Central relation

Individual problem

A lower-triangular factor has rows two, zero and one, two. Compute covariance and identify the restriction imposed by its upper-right zero.

A consequential failure

A Cholesky response is called causal without defending ordering, or a common shock is called identified network propagation.

Repair

Name the exclusion, timing, normalization, and alternative decompositions. Retain predictive claims when structural identification is incomplete.