Abstract
We generalize well‐known results on structural identifiability of vector autoregressive (VAR) models to the case where the innovation covariance matrix has reduced rank. Singular structural VAR models appear, for example, as solutions of rational expectation models where the number of shocks is usually smaller than the number of endogenous variables, and as an essential building block in dynamic factor models. We show that order conditions for identifiability are misleading in the singular case and we provide a rank condition for identifiability of the noise parameters. Since the Yule–Walker equations may have multiple solutions, we analyse the effect of restricting system parameters on over‐ and underidentification in detail and provide easily verifiable conditions.
Highlights
Singular structural vector autoregressive (SVAR) models play an important role in macroeconomic modelling
To prepare for the structural case where we will connect to external characteristics uniquely to the deep parameters, we review identifiability of the reduced form of singular VAR models, see Anderson et al (2012)
We derive a condition which ensures that the modeller imposed restrictions on the noise parameters do not contradict the singularity of the innovation covariance matrix
Summary
Singular structural vector autoregressive (SVAR) models play an important role in macroeconomic modelling. The singularity of the innovation covariance matrix has two possible consequences for the restrictions imposed by the modeller.. The restrictions imposed by the modeller might already be contained in the restrictions that are implicit due to the singularity structure of the innovation covariance matrix and are redundant. These cases must be taken into account when analysing identifiability properties of singular SVAR models. We focus on identifiability from second moment information, that is, the external characteristics correspond to the spectral density of the observed process (yt)
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