Multiple attractors and business fluctuations in a nonlinear macro-model with equity rationing

A stylized model of business fluctuations is developed, where investment and debt accumulation are responsible for the endogenous dynamics of income. Despite the simplicity of the model, the resulting nonlinear, two-dimensional discrete-time dynamical system displays a wide range of possible dynamic outcomes. If a key parameter, representing the propensity to invest, shifts exogenously from low to high values, a transition across qualitatively different long-run scenarios is observed, associated to different levels of economic activity. Moreover, coexistence of attractors and path-dependence characterize the dynamics for an intermediate range of such a parameter. The impact of exogenous disturbances on such situations results in aperiodic time series subject to unpredictable booms and slumps.