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

UTS Working Paper No. 123

26 Pages Posted: 2 Feb 2006

See all articles by Carl Chiarella

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group

Peter Flaschel

Bielefeld University - Department of Business Administration and Economics

Reiner Franke

Vienna University of Technology

Willi Semmler

The New School - Department of Economics; Universitaet Bielefeld; IIASA

Date Written: November 2002

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.

Keywords: real-financial interaction, higher-order local stability analysis, cascade of stable matricies, Tobin's average q, wage-price dynamics, Hopf bifurcation

JEL Classification: E12

Suggested Citation

Chiarella, Carl and Flaschel, Peter and Franke, Reiner and Semmler, Willi, Stability Analysis of a High-Dimensional Macrodynamic Model of Real-Financial Interaction: A Cascade of Matrices Approach (November 2002). UTS Working Paper No. 123. Available at SSRN: https://ssrn.com/abstract=880003 or http://dx.doi.org/10.2139/ssrn.880003

Carl Chiarella (Contact Author)

University of Technology, Sydney - UTS Business School, Finance Discipline Group ( email )

PO Box 123
Broadway, NSW 2007
Australia
+61 2 9514 7719 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.business.uts.edu.au/finance/

Peter Flaschel

Bielefeld University - Department of Business Administration and Economics ( email )

P.O. Box 100131
D-33501 Bielefeld, NRW 33501
Germany

Reiner Franke

Vienna University of Technology ( email )

Wien 1040
Austria

Willi Semmler

The New School - Department of Economics ( email )

65 Fifth Avenue
New York, NY 10003
United States

HOME PAGE: http://www.newschool.edu/nssr/faculty/?id=4e54-6b79-4e41-3d3d

Universitaet Bielefeld ( email )

Universit├Ątsstra├če 25
Bielefeld, NRW
Germany

IIASA ( email )

Schlossplatz 1
Laxenburg/Austria, A-2361
Austria

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