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arXiv · 2603.29178

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

Roberto Albarrán-García·Martha Alvarez-Ramírez·Carlos García-Azpeitia
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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.

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Roberto Albarrán-García, Martha Alvarez-Ramírez, Carlos García-Azpeitia. 2026-03-31. Endogenous Cycles in a Keen--Goodwin Model with Minsky Debt. https://arxiv.org/abs/2603.29178

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