Saddle Path Stability, Fluctuations and Indeterminacy in Economic Growth

STUDIES IN NONLINEAR DYNAMICS AND ECONOMETRICS, Vol. 1, No. 2

Posted: 24 Mar 1997

See all articles by Alfred Greiner

Alfred Greiner

Bielefeld University - Department of Business Administration and Economics

Willi Semmler

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

Abstract

We present a macroeconomic growth model in which investment in physical capital exhibits positive externalities which raise the stock of knowledge. Treating physical capital and knowledge as two separate variables, we show that the model can generate endogenous growth. It is demonstrated that there exist at most two balanced growth paths (BGPs) with endogenous growth. If the BGP is unique, it is always saddle-point stable. If there are two BGPs, the first is always stable in the saddle-point sense, whereas the second cannot be a saddle point. Instead, the second is either totally stable, giving rise to local indeterminacy, or completely unstable. Further, we can demonstrate that a Hopf bifurcation may occur at the second BGP, leading to persistent fluctuations. Besides local indeterminacy, the model may also give rise to global indeterminacy.

JEL Classification: O41

Suggested Citation

Greiner, Alfred and Semmler, Willi, Saddle Path Stability, Fluctuations and Indeterminacy in Economic Growth. STUDIES IN NONLINEAR DYNAMICS AND ECONOMETRICS, Vol. 1, No. 2. Available at SSRN: https://ssrn.com/abstract=3822

Alfred Greiner (Contact Author)

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

P.O. Box 100131
Bielefeld, 33501
Germany
+49 521 106 4859 (Phone)
+49 521 106 67120 (Fax)

HOME PAGE: http://phoenix.wiwi.uni-bielefeld.de/lehrbereiche/vwl/wipol

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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