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

We explore numerically 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 market and the degree of capital mobility , on the stability of equilibrium, and on the possible existence of business cycles. We determine by a numerical grid-search method the stability region in the parameter space and find that, by comparison to fixed exchange rates, flexible exchange rates cause increased stability of equilibrium with respect to variations of the model parameters. We identify analytically the Hopf-Neimark bifurcation curve along which business cycles may be generated, as well as the flip bifurcation curve along which period-doubling cascades leading to chaotic behavior are generated. We find that period-doubling cascades leading to chaos are the dominant behavior of the system of flexible exchange rates outside the stability region, persisting up to large values of the degree of capital mobility . 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 on the stability of equilibrium is also briefly discussed. Finally, we explore the special case (Model 2) incorporating the so-called wealth effect, which in the present case of flexible exchange rates is found to behave similarly to the basic model, contrary to the case of fixed exchange rates in which incorporation of the wealth effect causes an entirely different behavior of the system.