Abstract
We present a discrete two‐regional Kaldorian macrodynamic model with flexible exchange rates and explore numerically the stability of equilibrium and the possibility of generation of business cycles. We use a grid search method in two‐dimensional parameter subspaces, and coefficient criteria for the flip and Hopf bifurcation curves, to determine the stability region and its boundary curves in several parameter ranges. The model is characterized by enhanced stability of equilibrium, while its predominant asymptotic behavior when equilibrium is unstable is period doubling. Cycles are scarce and short‐lived in parameter space, occurring at large values of the degree of capital movement β. By contrast to the corresponding fixed exchange rates system, for cycles to occur sufficient amount of trade is required together with high levels of capital movement. Rapid changes in exchange rate expectations and decreased government expenditure are factors contributing to the creation of interregional cycles. Examples of bifurcation and Lyapunov exponent diagrams illustrating period doubling or cycles, and their development into chaotic attractors, are given. The paper illustrates the feasibility and effectiveness of the numerical approach for dynamical systems of moderately high dimensionality and several parameters.
Highlights
Aspects of international macroeconomics and regional economics are studied recently by methods of nonlinear economic dynamics see, e.g., 1–3
For prudent reactions by firms α < 1 equilibrium remains stable at high levels of capital movement even for high levels of trade transactions δ Figure 1
We presented a five-dimensional discrete two-regional Kaldorian macrodynamic model with flexible exchange rates, assuming similar economies of the two regions, and carried out a numerical exploration of its dynamical behavior, considering the effects of variation of the three basic parameters, namely, the common speed of adaptation of the goods markets α, the degree of capital mobility β, and the level of trade transactions between the regions δ
Summary
Aspects of international macroeconomics and regional economics are studied recently by methods of nonlinear economic dynamics see, e.g., 1–3. Interregional Kaldorian macrodynamic models of business cycles, based on trade interaction between the regions, have been studied by Lorenz 9 and Puu 2. We explore our two-regional macrodynamic model with flexible exchange rates focusing on the stability of equilibrium under variations of the model parameters and on the asymptotic behavior of the system outside the stability region, and consider in particular the possibility of occurrence of business cycles. Certain conclusions are drawn on the effects of the model parameters These regard mainly the size of the region of stability of equilibrium in parameter space, the possibility of occurrence of business cycles at reasonably small values of the interaction parameters, and the type of predominant asymptotic dynamical behavior of the system outside the stability region.
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