Endogenous cycles from income diversity, capital ownership, and differential savings

Endogenous cycles in standard growth models with capital accumulation of the Solow or the OLG type occur only when there is some degree of heterogeneity among consumers, differential savings, income diversity, or market specialization. Otherwise, without income effects or distribution effects long run steady states are mostly asymptotically stable predicting stable balanced growth for many of the commonly accepted growth models under most aggregative concave neoclassical production functions. This paper provides an attempt to exhibit a full richness of bifurcation scenarios for endogenously generated cycles using minimal extensions concerning preferences, technologies, and ownership of capital by extending the models of Kaldor, Pasinetti, and others to allow for ownership of capital among OLG consumers of workers and capitalists. It is shown that, under a sufficiently low but constant elasticity of substitution, the interaction of the nonlinear income distribution with heterogeneous logarithmic intertemporal preferences of consumers causes a variety of local bifurcation scenarios (Neimark–Sacker, fold, period doubling), multi-stability, as well as a rich variety of complex global dynamic features, such as homoclinic tangles, periodicity regions originating from Arnold tongues, closed curve attractors, and complex basins. The paper provides a detailed numerical analysis under a CES production scenario of several global bifurcations arising from heterogeneity which does not exist under the specific ownership restrictions imposed in the original Kaldor/Pasinetti models.