Chaotic and Fractal Evidence from Turkiye’s Macroeconomic System: Chaos-Augmented Phillips Curve

The paper explored the fractal, nonlinear and chaotic dynamics between oil prices, inflation, economic growth and unemployment in Turkiye from 1960 to 2024 and examined how energy market volatility propagated through the macroeconomy via complex, regime-dependent mechanisms. It developed a chaotic regression method and employed entropy-based measures (Shannon, Rényi and Tsallis), Lyapunov exponents, Lorenz and Rössler attractors, Julia set diagnostics and the chaos Granger causality test (Hiemstra–Jones). By nesting entropy, chaos and causality within a unified framework, it contributed methodological innovations and practical insights to the energy–economy literature. The chaotic regression results revealed that oil price shocks generated asymmetric and nonlinear responses in inflation, unemployment and growth that were characterized by chaos and sensitivity to initial conditions and demonstrated that oil shocks act as catalysts for nonlinear propagation and fractal macroeconomic dynamics. Julia set results determined that unemployment can be explained by inflation fractal size. Hiemstra–Jones method determined unidirectional causality from oil to both inflation, economic growth and unemployment. According to the results, adopting nonlinear and chaos-based modeling approaches is essential to understand the macroeconomic consequences of energy shocks. For policymakers, the evidence determined that the costs of disinflation or inflation control are sensitive to energy market volatility. The paper contributed to the energy–economy-econometrics literature by integrating entropy, chaos and causality analyses into the oil price–macroeconomy nexus by offering both methodological innovations and practical insights.