Unemployment–Wage Adjustment Dynamics in European Countries (2000–2025): A Complex Analytic Equilibrium Approach

This study develops a nonlinear macro-labor framework to analyze dynamic adjustment mechanisms in European labor markets using harmonic stability theory, panel econometric modeling, and frequency-domain propagation analysis. The research investigates whether labor market interactions exhibit partial harmonic conjugacy, asymmetric transmission structures, and regime-dependent convergence behavior. Employing panel VAR estimation, DCC-GARCH volatility modeling, threshold regression, structural break testing, and spectral coherence analysis, the study provides empirical evidence of nonlinear shock propagation and spatial heterogeneity across European economies.The results confirm the existence of partial harmonic equilibrium structures, where macro-labor variables satisfy local propagation symmetry but fail to maintain global analytic consistency under crisis conditions. Structural break analysis reveals significant regime shifts during the 2008 financial crisis and the COVID-19 shock. Convergence tests indicate fragmentation between core and peripheral economies, with peripheral regions exhibiting stronger persistence, higher crisis amplification, and slower adjustment speeds. Threshold regression results demonstrate state-dependent labor market responses, particularly under high unemployment regimes.Simulation and counterfactual policy analysis show that structural reforms and coordinated policy packages generate the largest welfare gains by reducing system instability and improving harmonic synchronization. Youth unemployment dynamics display higher volatility and stronger amplification effects, highlighting demographic vulnerability. Overall, the findings suggest that European macro-labor systems operate as nonlinear, spatially heterogeneous networks characterized by regime-switching propagation dynamics.The study contributes to nonlinear macroeconomics by introducing harmonic propagation analysis as a complementary framework for understanding labor market adjustment. Policy implications emphasize the importance of structural flexibility, institutional coordination, and crisis-response mechanisms in maintaining macroeconomic stability.