scholarly journals Numerical Exploration of Kaldorian Macrodynamics: Hopf-Neimark Bifurcations and Business Cycles with Fixed Exchange Rates

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Toichiro Asada ◽  
Christos Douskos ◽  
Panagiotis Markellos
Keyword(s):  
Business Cycles ◽  
Exchange Rates ◽  
Parameter Space ◽  
Open Economy ◽  
Capital Mobility ◽  
Complex Dynamics ◽  
Model Parameters ◽  
Bifurcation Curve ◽  
Fixed Exchange Rates ◽  
The Stability

We explore numerically a three-dimensional discrete-time Kaldorian macrodynamic model in an open economy with fixed exchange rates, focusing on the effects of variation of the model parameters, the speed of adjustment of the goods marketα, and the degree of capital mobilityβon the stability of equilibrium and on the existence of business cycles. We determine the stability region in the parameter space and find that increase ofαdestabilizes the equilibrium more quickly than increase ofβ. We determine the Hopf-Neimark bifurcation curve along which business cycles are generated, and discuss briefly the occurrence of Arnold tongues. Bifurcation and Lyapunov exponent diagrams are computed providing information on the emergence, persistence, and amplitude of the cycles and illustrating the complex dynamics involved. Examples of cycles and other attractors are presented. Finally, we discuss a two-dimensional variation of the model related to a “wealth effect,” called model 2, and show that in this case,αdoes not destabilize the equilibrium more quickly thanβ, and that a Hopf-Neimark bifurcation curve does not exist in the parameter space, therefore model 2 does not produce cycles.

scholarly journals Numerical Exploration of Kaldorian Macrodynamics: Enhanced Stability and Predominance of Period Doubling and Chaos with Flexible Exchange Rates

2008 ◽  
Vol 2008 ◽  
pp. 1-23 ◽  
Author(s):  
Toichiro Asada ◽  
Christos Douskos ◽  
Panagiotis Markellos
Keyword(s):  
Exchange Rates ◽  
Stability Region ◽  
Extreme Values ◽  
Period Doubling ◽  
Model Parameters ◽  
Flip Bifurcation ◽  
Bifurcation Curve ◽  
The Stability ◽  
Flexible Exchange Rates ◽  
Enhanced Stability

We explore a discrete Kaldorian macrodynamic model of an open economy with flexible exchange rates, focusing on the effects of variation of the model parameters, the speed of adjustment of the goods marketα, and the degree of capital mobilityβ. We determine by a numerical grid search method the stability region in parameter space and find that flexible rates cause enhanced stability of equilibrium with respect to variations of the parameters. We identify the Hopf-Neimark bifurcation curve and the flip bifurcation curve, and find that the period doubling cascades which leads to chaos is the dominant behavior of the system outside the stability region, persisting to large values ofβ. Cyclical behavior of noticeable presence is detected for some extreme values of a state parameter. Bifurcation and Lyapunov exponent diagrams are computed illustrating the complex dynamics involved. Examples of attractors and trajectories are presented. The effect of the speed of adaptation of the expected rate is also briefly discussed. Finally, we explore a special model variation incorporating the “wealth effect” which is found to behave similarly to the basic model, contrary to the model of fixed exchange rates in which incorporation of this effect causes an entirely different behavior.

The Stabilization of an Open Economy with Capital Controls: An Analysis Using Malaysian Data

2003 ◽  
Vol 2 (3) ◽  
pp. 63-83 ◽  
Author(s):  
Naoyuki Yoshino ◽  
Sahoko Kaji ◽  
Yoko Ibuka
Keyword(s):  
Exchange Rate ◽  
Exchange Rates ◽  
Open Economy ◽  
Exchange Rate Volatility ◽  
Capital Controls ◽  
Loss Functions ◽  
Economic Welfare ◽  
Real Gdp ◽  
Net Exports ◽  
Fixed Exchange Rates

The purpose of this paper is to analyze the effectiveness of capital controls and fixed exchange rates in improving economic welfare. We apply Malaysian data to our theoretical model and derive the following results for the period of our estimation. High exchange rate volatility negatively affects Malaysian net exports and real GDP. By stabilizing the exchange rate and recovering monetary policy autonomy, capital controls and fixed exchange rates can lead to lower values of loss functions. This beneficial effect is stronger, the more open the Malaysian economy.

scholarly journals A nonlinear macrodynamic model with fixed exchange rates: Its dynamics and noise effects

2000 ◽  
Vol 4 (4) ◽  
pp. 319-331 ◽  
Author(s):  
Toichiro Asada ◽  
Toichio Inaba ◽  
Tetsuya Misawa
Keyword(s):  
Exchange Rates ◽  
Open Economy ◽  
Chaotic Dynamics ◽  
Small Open Economy ◽  
Three Dimensional ◽  
Basic Structure ◽  
Stochastic Disturbances ◽  
Noise Effects ◽  
Fixed Exchange Rates ◽  
Linear Approximation Method

In this paper, we formulate a discrete time version of the Kaldorian macrodynamic model in a small open economy with fixed exchange rates. The model is described by a system of the three-dimensional nonlinear difference equations with and without stochastic disturbances (noise effects). We study the local stability/instability properties analytically by using the linear approximation method, and chaotic dynamics with and without noise effects are investigated by means of numerical simulations. In general, it is believed that the effect of the noise is to obscure the basic structure of the system. But, this is not necessarily the case. We show by means of numerical analysis that the noise can reveal the hidden structure of the model contrary to the usual intuition in some situations.

scholarly journals Can business cycles arise in a two-regional model with fixed exchange rates?

2009 ◽  
Vol 43 (1) ◽  
pp. 123-135
Author(s):  
Peter Maličká ◽  
Rudolf Zimka
Keyword(s):  
Business Cycles ◽  
Exchange Rates ◽  
Linear Approximation ◽  
Capital Stock ◽  
Sufficient Conditions ◽  
Regional Model ◽  
Dimensional Model ◽  
Money Stock ◽  
Fixed Exchange Rates ◽  
Five Dimensional Model

Abstract The two-regional five dimensional model describing the development of income, capital stock and money stock, which was introduced by T. Asada in [A Two-regional Model of Business Cycles with Fixed ExchangeRates: A Kaldorian Approach, Discuss. Paper Ser., No. 44, Chuo University, Tokyo, Japan, 2003] is analysed. Sufficient conditions for the existence of one pair of purely imaginary eigenvalues and three eigenvalues with negative real parts in the linear approximation matrix of the model are found. Theorem on the existence of business cycles is presented.

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