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| Title: | | A unique orthogonal variance decomposition  |
| Authors: | | Wong, Woon K. |
| Issue Date: | | 2008 |
| Series/Report no.: | | Cardiff Economics Working Papers E2008/10 |
| Abstract: | | Let 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[...] , the square root of Σ. |
| Subjects: | | Variance decomposition Cholesky decomposition unique orthogonal decomposition and square root matrix |
| JEL: | | C01 |
| Document Type: | | Working Paper |
| Appears in Collections: | | Cardiff Economics Working Papers
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