Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference

TLDR

Structural vector autoregressions (SVARs) are widely used for policy analysis, yet no practical rank conditions exist to guarantee global identification, and efficient small‑sample estimation algorithms for nonlinear restrictions are lacking. This paper contributes four advances: establishing general rank conditions for global identification, demonstrating their easy implementation for linear and certain nonlinear restrictions, showing that exact‑identification conditions reduce to a simple counting exercise, and developing efficient small‑sample estimation and inference algorithms for SVARs with nonlinear restrictions. The authors derive sufficient rank conditions for general identification and necessary and sufficient conditions for exact identification, prove these can be implemented straightforwardly for a broad class of restrictions, reduce exact‑identification to a counting exercise, and present efficient algorithms for small‑sample estimation and inference, particularly under nonlinear restrictions.

Abstract

Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic stochastic general equilibrium (DSGE) models; yet no workable rank conditions to ascertain whether an SVAR is globally identified have been established. Moreover, when nonlinear identifying restrictions are used, no efficient algorithms exist for small-sample estimation and inference. This paper makes four contributions towards filling these important gaps in the literature. First, we establish general rank conditions for global identification of both identified and exactly identified models. These rank conditions are sufficient for general identification and are necessary and sufficient for exact identification. Second, we show that these conditions can be easily implemented and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we show that the rank condition for exactly identified models amounts to a straightforward counting exercise. Fourth, we develop efficient algorithms for small-sample estimation and inference, especially for SVARs with nonlinear restrictions.