  When in proxy-SVARs the covariance matrix of VAR disturbances is subject to
exogenous, permanent, nonrecurring breaks that generate target impulse response
functions (IRFs) that change across volatility regimes, even strong, exogenous
external instruments can result in inconsistent estimates of the dynamic causal
effects of interest if the breaks are not properly accounted for. In such
cases, it is essential to explicitly incorporate the shifts in unconditional
volatility in order to point-identify the target structural shocks and possibly
restore consistency. We demonstrate that, under a necessary and sufficient rank
condition that leverages moments implied by changes in volatility, the target
IRFs can be point-identified and consistently estimated. Importantly, standard
asymptotic inference remains valid in this context despite (i) the covariance
between the proxies and the instrumented structural shocks being local-to-zero,
as in Staiger and Stock (1997), and (ii) the potential failure of instrument
exogeneity. We introduce a novel identification strategy that appropriately
combines external instruments with "informative" changes in volatility, thus
obviating the need to assume proxy relevance and exogeneity in estimation. We
illustrate the effectiveness of the suggested method by revisiting a fiscal
proxy-SVAR previously estimated in the literature, complementing the fiscal
instruments with information derived from the massive reduction in volatility
observed in the transition from the Great Inflation to the Great Moderation
regimes.
