A Unique Orthogonal Variance Decomposition

Woon K. Wong ()

No E2008/10, Cardiff Economics Working Papers from Cardiff University, Cardiff Business School, Economics Section

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^1/2, the square root of Σ.

Keywords: Variance decomposition; Cholesky decomposition; unique orthogonal decomposition and square root matrix (search for similar items in EconPapers)
JEL-codes: C01 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-bec and nep-ecm
Date: 2008-04
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Persistent link: http://EconPapers.repec.org/RePEc:cdf:wpaper:2008/10

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