Nonlinear Inflation Dynamics and Policy Feedback: Evidence of Hopf Bifurcation in the Euro Area (2000–2025)

This paper investigates the transition of euro area inflation dynamics from a stable regime to persistent cyclical behavior through the lens of nonlinear macroeconomic theory. We develop and estimate a nonlinear New Keynesian Phillips Curve (NKPC) model augmented with endogenous monetary policy feedback and regime-dependent dynamics. The analysis shows that increasing Phillips curve convexity, rising inflation persistence, and variations in policy responsiveness can push the system through a Hopf bifurcation, leading to the emergence of endogenous limit cycles. Empirical results based on euro area data (2000–2025) confirm significant nonlinearities, structural breaks around major crisis episodes, and a narrowing stability margin over time. Robustness checks—including alternative inflation measures, estimation methods, subsample tests, and country-group heterogeneity—support the central findings. Welfare comparisons across alternative policy rules indicate that nonlinear dynamics alter the ranking of monetary strategies and that aggressive policy responses are not universally stabilizing. The results provide a unified explanation for the euro area’s regime transitions and offer concrete guidance for central bank design in environments characterized by structural nonlinearities and shock amplification.