Keen model with a delayed Phillips curve

Hyman Minsky has put forth that financial crises are inherent to the structure of capitalist economic system, claiming that periods of stability will naturally lead to instability. The simple main reason is that over time, economic agents take on increasing levels of risk and debt, ultimately triggering financial breakdowns. Steve Keen developed a mathematical model that represents the interactions between wage share, employment rate, and debt dynamics that can reflect Minsky's ideas. His model simulates how extreme borrowing may result in destabilization of an economy, offering a powerful alternative to traditional equilibrium-based economics. In this article we consider an extended Keen model which takes into account a variable price level and we modify it by introducing a delay in the Phillips curve. Our results show that, in a situation where the non-delay system predicts a stable regime, under the same economic conditions, the delayed mechanism may experience periodic oscillations and instability in wage share, employment rate, and debt ratio. From an economic perspective, this corresponds to the emergence of endogenous cyclical dynamics instead of a stable regime, thereby restoring Goodwin-type cycles within the modified Keen framework.