A Unique Orthogonal Variance Decomposition
AbstractLet e and Σ be respectively the vector of shocks and its variance covariance matrix in a linear system of equations in reduced form. This article shows that a unique orthogonal variance decomposition can be obtained if we impose a restriction that maximizes the trace of A, a positive definite matrix such that Az = e where z is vector of uncorrelated shocks with unit variance. Such a restriction is meaningful in that it associates the largest possible weight for each element in e with its corresponding element in z. It turns out that A = Σ 1/2 , the square root of Σ.
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Bibliographic InfoPaper provided by Cardiff University, Cardiff Business School, Economics Section in its series Cardiff Economics Working Papers with number E2008/10.
Length: 19 pages
Date of creation: Apr 2008
Date of revision:
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Variance decomposition; Cholesky decomposition; unique orthogonal decomposition and square root matrix;
Find related papers by JEL classification:
- C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-05-05 (All new papers)
- NEP-BEC-2008-05-05 (Business Economics)
- NEP-ECM-2008-05-05 (Econometrics)
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