On dynamics in a medium-term Keynesian model

Abstract

This paper rigorously examines the (in)stability of limit cycles generated by Hopf bifurcations in a medium-term Keynesian model. The bifurcation equation of the model is derived and the conditions for stable and unstable limit cycles are presented. Numerical simulations are performed to illustrate the analytical results.

Structural Stability Analysis in a Dynamic IS-LM-AS Macroeconomic Model with Inflation Expectations

“…However, the linearity of the system of ordinary differential equations (ODEs) governing the dynamics of our model prevents the occurrence of limit cycles ( ere are dynamic models in the business cycle literature, which use the Poincaré-Bendixson theorem as an analytical tool to verify the existence of limit cycles (Chang and Smyth [16]; Dana & Malgrange [17]; Schinasi [18]; Semmler [19]). However, this theorem cannot be applied to three-dimensional or higher order dynamical systems, but in the literature also, there are several papers that have used the Hopf bifurcation theorem (Poincaré-Andronov-Hopf theorem) to verify the existence of business cycles in nonlinear dynamic models [11,[20][21][22][23][24][25][26][27][28][29][30]).…”

“…Nozaki (see [11]) used α 0.3 in simulations of dynamic IS-LM-PC models. Murakami and Zimka (see [26]) used α 0.3, ε 1.2, β 0.12, and h 0.2 in the computational simulations of a medium-term dynamic Keynesian model. In addition, Moroney (see [36]) reported that, for the period 1980-1993 and for a group of 21 countries with an average GDP growth rate of 2.4% and with an average ination rate of 2.9%, the average money growth rate amounted to 5.9%.…”