Identification of Covariance Structures
The issue of identification of covariance structures, which arises in a number of different contexts, has been so far linked to conditions on the true parameters to be estimated. In this paper, this limitation is removed. As done by Johansen (1995) in the context of linear models, the present paper provides necessary and sufficient conditions for the identification of a covariance structure that depend only on the constraints, and can therefore be checked independently of estimated parameters. A sufficient condition is developed, which only depends on the structure of the constraints. It is shown that this structure condition, if coupled with the familiar order condition, provides a sufficient condition for identification. In practice, since the structure condition holds if and only if a certain matrix, constructed from the constraint matrices, is invertible, automatic software checking for identification is feasible even for large-scale systems.
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- Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
- Johansen, Soren, 1995. "Identifying restrictions of linear equations with applications to simultaneous equations and cointegration," Journal of Econometrics, Elsevier, vol. 69(1), pages 111-132, September.
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