Shocks or Shifts? Identifying Macroeconomic Impulse Responses with Instruments

This paper studies how normalization choices shape identification and inference for instrumented impulse responses. Point-estimate IRFs are often treated as rescalable across normalizations, but this is not true for inference: different normalizations define different estimands and different weak-instrument problems. I show that standard SVAR-IV and LP-IV estimators can be read in two ways. Under structural-shock assumptions, they estimate impulse responses to latent shocks, normalized through an observed impact variable. Under weaker reduced-form IV assumptions, the same ratio estimators instead identify causal responses to exogenous shifts in that observed variable. This distinction matters empirically. Impact-normalized inference can become weak when the instrument has little covariance with the chosen normalization variable, even if it is informative about the latent shock. One-standard-deviation IRFs use the structural-shock restrictions more directly, avoid choosing an anchor variable, and can deliver substantially shorter intervals under weak normalization. I therefore propose a shock-based relevance diagnostic that targets the primitive relevance condition for the latent shock rather than an arbitrary normalization equation.

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