Endogenous desired debt in a Minskyan business model

We consider a Minskyan type model of a closed economy with autonomous public expenditure formulated in a discrete time framework, where an endogenous debt adjustment process is considered and where income variations account for real world physical and social constraints. The model is characterized by a unique nontrivial fixed point matching the economic equilibrium. We study its stability properties in terms of the constant factor that fixes the firms' desired debt level at a certain proportion of the current income. The stability loss of the fixed point is associated with either a subcritical flip or a supercritical Neimark-Sacker bifurcation. The latter implies occurrence of self-sustained oscillations interpreted as business cycles. We present three possible dynamic scenarios right after the Neimark-Sacker bifurcation: in a generic case and in two resonant cases. We also describe modifications of the attractor when propensity of firms to get into debt grows. In addition, we highlight that the increase of instabilities and complexities of dynamic outcomes is paired with the rise of the so called financial fragility indicator, which is a measure of fragility of the financial structure of the economy.