“Stable endogenous cycles in a non-Kaldorian IS-LM model with a negative interest elasticity of savings

Using an explicit center manifold reduction in correspondence of a Bogdanov-Takens singularity, we are able to derive a simplified two-dimensional framework to explore the global dynamics of the intermediate-run, IS-LM model of Schinasi's type, with pure money financing of the budget deficits. This system has long served as a prototype for the study of deterministic business cycle fluctuations arising in the neighbourhood of the steady-state. This literature, however, develops inside the so-called "Kaldorian tradition" which, starting from the S-shaped investment function, relies on a greater-than-unity marginal propensity to spend over the cycle. Our results, assuming a negative interest elasticity of savings, innovate the literature in what follows. First, for a set of parameter values close to the bifurcation levels, we find that two steady-states can emerge, one of saddle-type and one of non-saddle-type. The non-saddle steady state fulfils standard Kaldorian assumptions, whereas the saddle steady-state does not require any assumption on the marginal propensity to spend over the cycle. Second, for a further specification of the parameter values, there exists a family of supercritical closed orbits, Hopf-bifurcating around the non-saddle steady state which are approached by either trajectories originating nearby the non-saddle steady state (the Kaldorian economy) or by trajectories originating nearby the saddle steady-state (the non-Kaldorian economy). This implies that the IS-LM model can lead to oscillating solutions even when the marginal propensity to spend is smaller than one.