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Wong, Woon K.
Year of Publication: 
Series/Report no.: 
Cardiff Economics Working Papers E2008/10
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.
Variance decomposition
Cholesky decomposition
unique orthogonal decomposition and square root matrix
Document Type: 
Working Paper

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