Robust proxy-SVAR identification with invalid instruments under weak volatility shifts

Develop a comprehensive and robust identification and estimation framework for proxy-identified structural VARs (proxy-SVARs) that fully integrates potentially invalid external instruments in settings where the change in unconditional volatility across regimes provides limited identification information (i.e., when the difference between regime-specific covariance matrices is small or shrinking), so that standard stability-restriction rank conditions may fail to deliver reliable identification.

Background

The paper shows that when unconditional volatility shifts are informative and suitable stability restrictions are imposed, target impulse responses in proxy-SVARs are point-identified and can be estimated consistently, even if instruments are weak or contaminated. Identification is characterized by a necessary and sufficient Jacobian rank condition linking reduced-form and structural parameters across volatility regimes.

However, the authors note that identification may fail when volatility shifts are not sufficiently informative—formally, when the difference between regime-specific covariance matrices shrinks, leading to a weak volatility shift. In such cases, the available information from volatility changes may not compensate for instrument invalidity, and the standard approach may break down.

In this context, the authors explicitly leave for future research the development of a comprehensive and robust approach that can handle potentially invalid instruments when volatility shifts provide limited identification information, beyond the diagnostics they discuss (e.g., ex-post assessment of the Jacobian rank).

References

We leave for future research the development of a comprehensive and robust approach to proxy-SVARs that fully integrates potentially invalid external instruments in situations where the volatility shifts provide limited identification information.

— Invalid proxies and volatility changes  (2403.08753 - Angelini et al., 2024) in Main paper, Section “Proxy-SVARs with Stability Restrictions,” Identification subsection, footnote following the discussion of identification failures under weak volatility shifts

What we do not establish is their key condition --- that a cross-surface index responds to episode state while remaining unaffected by the focal event; excluding the event's own surface makes that plausible, co-activity keeps it an assumption. Testing it is the most direct route from these diagnostics to an estimator, and we leave it open.

— Event-Time Confounding Under Bursty Human Dynamics  (2608.21294 - Iannelli et al., 21 Aug 2026) in Section 2, paragraph “Negative controls and proxies for unmeasured confounding”