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‘Jumps’ In Macroeconomic Models: An Example When Eigenvalues Are Complex‐Valued

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  • PETER J. STEMP

Abstract

The dynamic properties of continuous‐time 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. Assuming no zero eigenvalues and that all eigenvalues are distinct, this also means that the number of predetermined variables, otherwise referred to as continuous or non‐ ‘jump’ variables, must equal the number of stable eigenvalues. In this paper, we investigate the application of the Blanchard and Kahn results and establish that these results also carry through for linear dynamical systems where some of the eigenvalues are complex‐valued. An example with just one complex conjugate pair of stable eigenvalues is presented. The Appendix contains a general n‐dimensional model.

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  • Peter J. Stemp, 2006. "‘Jumps’ In Macroeconomic Models: An Example When Eigenvalues Are Complex‐Valued," Australian Economic Papers, Wiley Blackwell, vol. 45(4), pages 333-342, December.
    • Handle: RePEc:bla:ausecp:v:45:y:2006:i:4:p:333-342
    DOI: 10.1111/j.1467-8454.2006.00297.x
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    1. Dornbusch, Rudiger, 1976. "Expectations and Exchange Rate Dynamics," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1161-1176, December.
    2. Peter J. Stemp, 2004. "A Review of 'Jumps' in Macroeconomic Models: With Special Reference to the Case when Eigenvalues are Complex-Valued," Department of Economics - Working Papers Series 920, The University of Melbourne.
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