Identifiability of Structural Singular Vector Autoregressive Models

TL;DR

This paper extends the theory of structural identifiability in vector autoregressive models to cases with reduced-rank innovation covariance matrices, crucial for models with fewer shocks than variables.

Contribution

It introduces a rank condition for identifiability in singular VAR models, addressing limitations of traditional order conditions and analyzing the impact of parameter restrictions.

Findings

Provides a rank-based criterion for identifiability in singular VAR models.

Shows traditional order conditions are misleading in the singular case.

Analyzes how restrictions affect over- and underidentification.

Abstract

We generalize well-known results on structural identifiability of vector autoregressive models (VAR) to the case where the innovation covariance matrix has reduced rank. Structural singular 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 provide a rank condition for identifiability of the noise parameters. Since the Yule-Walker equations may have multiple solutions, we analyze the effect of restrictions on the system parameters on over- and underidentification in detail and provide easily verifiable conditions.