Partially identified heteroskedastic SVARs

This paper presents new results on the identification of heteroskedastic structural vector autoregressive (HSVAR) models. Point identification of HSVAR models fails when some shifts in the variances of the structural shocks are suspected to be statistically indistinguishable from each other. This paper presents a new strategy that allows researchers to continue using HSVAR models in this empirically relevant case. We show that a combination of heteroskedasticity and zero restrictions can recover point identification in HSVAR models even in the absence of heterogeneous variance shifts. We derive the identified sets for impulse responses and show how to compute them. We perform inference on the impulse response functions, building on the robust Bayesian approach developed for set-identified SVARs. To illustrate our proposal, we present an empirical example based on the literature on the global crude oil market, where standard identification is expected to fail under heteroskedasticity.