When in proxy-SVARs the external instruments used to identify structural shocks are "weak", asymptotically correct inference on the target impulse response functions (IRFs) requires weak-instrument robust methods. Even with strong proxies, the IRFs cannot be estimated consistently if the exogeneity condition fails, i.e. if the proxies are correlated with a subset of the non-instrumented structural shocks.

We show that in the presence of exogenous, permanent (nonrecurring) breaks in the VAR error covariance matrix that generates distinct volatility regimes in the data, the responses of interest can be point-identified and estimated consistently, and standard inference applies despite (i) the covariance between the proxies and the instrumented structural shocks is local-to-zeroas in Staiger and Stock (1997), (ii) instruments exogeneity possibly fails.

These results hold regardless of whether IRFs are assumed constant across volatility regimes, or can possibly change across them, our leading case of interest. The rationale of this result is that if the moment conditions provided by the changes in volatility suffice to point-identify the target structural shocks, the moment conditions associated with the proxies, even potentially invalid proxies, do not alter the necessary rank condition for identification and do not affect the consistency of the extremum estimator being considered.

We propose a novel identification strategy for SVARs in which the external instruments are combined with changes in volatility regimes, without the need to assume their relevance and exogeneity. We illustrate the usefulness of the suggested method by revisiting some proxy-SVARs estimated in the extant literature.

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