Identification or Propagation? Shock-Based Weak-IV Diagnostics and Bootstrap Inference for Instrumented VARs
This paper documents an inconsistency in prevailing practice: instrument relevance in structural VARs is often assessed using an anchor equation’s reduced-form residual rather than the identified structural shock. As a result, the test is anchor-dependent and does not directly target the moment condition underlying identification. I propose a shock-based, anchor-independent weak instrument test based on the usual $F$-statistic—together with a bootstrap procedure that normalizes sign on the recovered shock—that yields invariant and stronger diagnostics, as well as typically tighter inference. I also show that when SVARs produce “structural’’ IRFs that are statistically indistinguishable from reduced-form dynamic multipliers, the instrument is likely weak, mis-specified, or simply superfluous.