  In this paper we propose a class of structural vector autoregressions (SVARs)
characterized by structural breaks (SVAR-WB). Together with standard
restrictions on the parameters and on functions of them, we also consider
constraints across the different regimes. Such constraints can be either (a) in
the form of stability restrictions, indicating that not all the parameters or
impulse responses are subject to structural changes, or (b) in terms of
inequalities regarding particular characteristics of the SVAR-WB across the
regimes. We show that all these kinds of restrictions provide benefits in terms
of identification. We derive conditions for point and set identification of the
structural parameters of the SVAR-WB, mixing equality, sign, rank and stability
restrictions, as well as constraints on forecast error variances (FEVs). As
point identification, when achieved, holds locally but not globally, there will
be a set of isolated structural parameters that are observationally equivalent
in the parametric space. In this respect, both common frequentist and Bayesian
approaches produce unreliable inference as the former focuses on just one of
these observationally equivalent points, while for the latter on a
non-vanishing sensitivity to the prior. To overcome these issues, we propose
alternative approaches for estimation and inference that account for all
admissible observationally equivalent structural parameters. Moreover, we
develop a pure Bayesian and a robust Bayesian approach for doing inference in
set-identified SVAR-WBs. Both the theory of identification and inference are
illustrated through a set of examples and an empirical application on the
transmission of US monetary policy over the great inflation and great
moderation regimes.
