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Stability Analysis of a High-Dimensional Macrodynamic Model of Real-Financial Interaction: A Cascade of Matrices Approach

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Abstract

This paper analyzes a high-dimensional macrodynamic model of the real-financial interaction. Regarding the financial sector it focuses on the stock market dynamics, whilst for the real sector it details goods market disequilibrium and two Phillips curves for prices as well as wages. The central link between the two sectors is constituted by Tobin's (average) q. The integrated dynamics of the model constitute a seven-dimensional system of differential equations, the stability analysis of which is the main contribution of the paper. The analysis proceeds by constructing a cascade of stable matrices and thus demonstrating that the long-run equilibrium is locally stable if certain adjustments are sufficiently sluggish. Large values of some reaction parameters, on the other hand, can destabilize the economy, while a Hopf bifurcation analysis shows the potential for cyclical motion in such circumstances.

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  • Carl Chiarella & Peter Flaschel & Reiner Franke & Willi Semmler, 2002. "Stability Analysis of a High-Dimensional Macrodynamic Model of Real-Financial Interaction: A Cascade of Matrices Approach," Working Paper Series 123, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  • Handle: RePEc:uts:wpaper:123
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    File URL: http://www.finance.uts.edu.au/research/wpapers/wp123.pdf
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    References listed on IDEAS

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    1. Chiarella,Carl & Flaschel,Peter, 2011. "The Dynamics of Keynesian Monetary Growth," Cambridge Books, Cambridge University Press, number 9780521180184.
    2. Evans, Martin & Wachtel, Paul, 1993. "Inflation Regimes and the," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 25(3), pages 475-511, August.
    3. Blanchard, Olivier J, 1981. "Output, the Stock Market, and Interest Rates," American Economic Review, American Economic Association, vol. 71(1), pages 132-143, March.
    4. Franke, Reiner & Sethi, Rajiv, 1998. "Cautious trend-seeking and complex asset price dynamics," Research in Economics, Elsevier, vol. 52(1), pages 61-79, March.
    5. Ricardo J. Caballero & John V. Leahy, 1996. "Fixed Costs: The Demise of Marginal q," NBER Working Papers 5508, National Bureau of Economic Research, Inc.
    6. Franke, Reiner, 1996. "A Metzlerian model of inventory growth cycles," Structural Change and Economic Dynamics, Elsevier, vol. 7(2), pages 243-262, June.
    7. Sethi, Rajiv, 1996. "Endogenous regime switching in speculative markets," Structural Change and Economic Dynamics, Elsevier, vol. 7(1), pages 99-118, March.
    8. Carl Chiarella & Peter Flaschel & Willi Semmler, 2001. "Real-Financial Interaction: A Reconsideration of the Blanchard Model with a State-of-Market Dependent Reaction Coefficient," Working Paper Series 111, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    9. H. Rose, 1967. "On the Non-Linear Theory of the Employment Cycle," Review of Economic Studies, Oxford University Press, vol. 34(2), pages 153-173.
    10. Alan Kirman, 2006. "Heterogeneity in Economics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(1), pages 89-117, May.
    11. Reiner Franke & Willi Semmler, 1999. "Bond Rate, Loan Rate and Tobin's q in a Temporary Equilibrium Model of the Financial Sector," Metroeconomica, Wiley Blackwell, vol. 50(3), pages 351-385, October.
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    Cited by:

    1. Asada, Toichiro & Chen, Pu & Chiarella, Carl & Flaschel, Peter, 2006. "Keynesian dynamics and the wage-price spiral: A baseline disequilibrium model," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 90-130, March.
    2. Toichiro Asada & Carl Chiarella & Peter Flaschel, 2003. "Keynes-Metzler-Goodwin Model Building: The Closed Economy," Working Paper Series 124, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    3. Carl Chiarella & Peter Flaschel & Reiner Franke & Willi Semmler, 2003. "Output and the Term Structure of Interest Rates: Ways Out of th Jump-Variable Conundrum," Working Paper Series 125, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    4. T. Asada & P. Chen, 2004. "Keynesian Dynamics and the wage price spiral. A baseline disequilibrium approach," Computing in Economics and Finance 2004 262, Society for Computational Economics.
    5. Carl Chiarella & Peter Flaschel & Willi Semmler, 2003. "Real-Financial Interaction: Implications of Budget Equations and Capital Accumulation," Working Paper Series 127, Finance Discipline Group, UTS Business School, University of Technology, Sydney.

    More about this item

    Keywords

    real-financial interaction; higher-order local stability analysis; cascade of stable matrices; tobin's average q; wage-price dynamics; hopf bifurcation;

    JEL classification:

    • E12 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Keynes; Keynesian; Post-Keynesian

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