Endogenous Cycles in a Keen--Goodwin Model with Minsky Debt

TL;DR

This paper studies a Keen--Goodwin model incorporating Minsky debt, revealing how interest rates influence endogenous business cycles through analytical and numerical methods.

Contribution

It derives explicit conditions for cycle emergence and analyzes the impact of interest rates on endogenous economic fluctuations.

Findings

Interest rates determine and modulate endogenous cycles.

Explicit Hopf bifurcation condition derived.

Numerical simulations support analytical predictions.

Abstract

We analyze a three-dimensional Keen--Goodwin model that couples wage--employment dynamics with Minsky-style private debt. At zero real interest the interior equilibrium is nonhyperbolic and organized by a two-dimensional center manifold foliated by neutral Goodwin cycles. Introducing a small positive interest rate unfolds this degeneracy: we derive an explicit Hopf condition, prove persistence of the center manifold as a normally hyperbolic attracting surface, and obtain first-order amplitude and frequency corrections for the emergent limit cycle via phase--amplitude reduction. Numerical simulations support the asymptotic predictions and demonstrate how interest rates determine and modulate endogenous business cycles.