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Chapter 11 A High-Dimensional Model of Real-Financial Market Interaction: The Cascade of Stable Matrices Approach

Elsevier Science & Technology
Publication Date
DOI: 10.1016/s0573-8555(05)77011-5
  • Real-Financial Interaction
  • Higher-Order Local Stability Analysis
  • Cascade Of Stable Matrices
  • Tobin'S Average [Formula Omitted]
  • Wage-Price Dynamics
  • Hopf Bifurcation
  • Mathematics


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, while 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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