| | A Review of 'Jumps' in Macroeconomic Models: With Special Reference to the Case when Eigenvalues are Complex-Valued ... (Site not responding. Last check: 2007-11-07) |
 | | The dynamic properties of macroeconomic models are typically characterised by having a combination of stable and unstable eigenvalues. |
 | | In a seminal paper, Blanchard and Kahn showed that, for linear models, in order to ensure a unique solution, the number of discontinuous or “jump” variables must equal the number of unstable eigenvalues in the economy. |
 | | We show that the crucial reason why the results continue to hold for complex-valued eigenvalues is because, in order to ensure that the solutions for the endogenous variables are real-valued and thus have an economic interpretation, the coefficients associated with each complex conjugate pair of eigenvalues must also come in complex conjugate pairs. |
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