Evaluating the Number of Zero Eigenvalues in a Dynamic Model. In J. Gr uber (Ed.) ECONOMETRIC DECISION MODELS.

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Abstract: If a sparse matrix can be put into a block triangular form its eigenvalues can simply be computed from the submatrices on the diagonal and most zero eigenvalues are recognized without numerical computations. It is shown how to find the block triangular form of a dynamic multiplier matrix based only upon the causal content of the coefficient matrices. For the indecomposable matrices on the diagonal additional zero eigenvalues may also be identified on a qualitative basis. Moreover the approach provides insight on which coefficients are relevant for the existence of eigenvalues and which coefficients are not.

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