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Atlanta Fed Working Papers


Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference

Juan F. Rubio-Ramírez, Daniel F.Waggoner, and Tao Zha
Working Paper 2008-18
September 2008

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Structural vector autoregressions (SVARs) are widely used for policy analysis and to provide stylized facts for dynamic general equilibrium models. Yet there have been no workable rank conditions to ascertain whether an SVAR is globally identified. When identifying restrictions such as long-run restrictions are imposed on impulse responses, there have been no efficient algorithms for small-sample estimation and inference. To fill these important gaps in the literature, this paper makes four contributions. First, we establish general rank conditions for global identification of both overidentified and exactly identified models. Second, we show that these conditions can be checked as a simple matrix-filling exercise and that they apply to a wide class of identifying restrictions, including linear and certain nonlinear restrictions. Third, we establish a very simple rank condition for exactly identified models that amounts to a straightforward counting exercise. Fourth, we develop a number of efficient algorithms for small-sample estimation and inference.

JEL classification: C32, E50

Key words: linear and nonlinear restrictions, global identification, almost everywhere, rank conditions, orthogonal rotation, transformation, simultaneity


The authors thank Jushan Bai, Fabio Canova, John Chao, Xiaohong Chen, Tim Cogley, Wouter Den Haan, Jean-Marie Dufour, Jon Faust, Cheng Hsiao, Roger Moon, Jim Nason, Chris Otrok, Adrian Pagan, Ingmar Prucha, John Rust, and Harald Uhlig for helpful discussions and comments. The current version of this paper draws heavily from two unpublished manuscripts: "Markov-Switching Structural Vector Autoregressions: Theory and Application" by Rubio-Ramírez, Waggoner, and Zha and "Identification Issues in Vector Autoregressions" by Waggoner and Zha. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Juan F. Rubio-Ramírez, Economics Department, Duke University, P.O. Box 90097, Durham, NC, 27708, 919-660-1865, juan.rubio-ramirez@duke.edu; Daniel F. Waggoner, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8278, daniel.f.waggoner@atl.frb.org; or Tao Zha, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8353, tzha@earthlink.net.

For further information, contact the Public Affairs Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, Georgia 30309-4470, 404-498-8020.