An Extended Goodwin Model with Endogenous Technical Change: Theory and Simulation for the US Economy (1960-2019)

Cajas Guijarro, John (2023): An Extended Goodwin Model with Endogenous Technical Change: Theory and Simulation for the US Economy (1960-2019).

Abstract

This paper extends the two-dimensional Goodwin model of distributive cycles by incorporating endogenous technical change, inspired on some insights originally formulated by Marx. We introduce a three-dimensional dynamical system, expanding the model to include wage share, employment rate, and capital-output ratio as state variables. Theoretical analysis demonstrates an economically meaningful and locally stable equilibrium point, and the Hopf bifurcation theorem reveals the emergence of stable limit cycles as the mechanization-productivity elasticity surpasses a critical value. Econometric estimation of model parameters using ARDL bounds cointegration tests is performed for the US economy from 1965 to 2019. Simulations show damped oscillations, limit cycles, and unstable oscillations, contributing to the understanding of complex capitalist dynamics.

• Item Type: MPRA Paper
• Language: English
• Keywords: Goodwin model, endogenous technical change, Hopf bifurcation, ARDL, numerical simulations
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E11 - Marxian ; Sraffian ; Kaleckian; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles; O - Economic Development, Innovation, Technological Change, and Growth > O3 - Innovation ; Research and Development ; Technological Change ; Intellectual Property Rights > O33 - Technological Change: Choices and Consequences ; Diffusion Processes; O - Economic Development, Innovation, Technological Change, and Growth > O4 - Economic Growth and Aggregate Productivity > O41 - One, Two, and Multisector Growth Models

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