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

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  • Cajas Guijarro, John

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.

Suggested Citation

  • Cajas Guijarro, John, 2023. "An Extended Goodwin Model with Endogenous Technical Change: Theory and Simulation for the US Economy (1960-2019)," MPRA Paper 118878, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:118878
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    References listed on IDEAS

    as
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    3. Araujo, Ricardo Azevedo & Dávila-Fernández, Marwil J. & Moreira, Helmar Nunes, 2019. "Some new insights on the empirics of Goodwin's growth-cycle model," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 42-54.
    4. Harris, Donald J, 1983. "Accumulation of Capital and the Rate of Profit in Marxian Theory," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 7(3-4), pages 311-330, September.
    5. Jose Barrales‐Ruiz & Ivan Mendieta‐Muñoz & Codrina Rada & Daniele Tavani & Rudiger von Arnim, 2022. "The distributive cycle: Evidence and current debates," Journal of Economic Surveys, Wiley Blackwell, vol. 36(2), pages 468-503, April.
    6. Grassetti, F. & Guzowska, M. & Michetti, E., 2020. "A dynamically consistent discretization method for Goodwin model," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    7. Eagly, Robert V, 1972. "A Macro Model of the Endogenous Business Cycle in Marxist Analysis," Journal of Political Economy, University of Chicago Press, vol. 80(3), pages 523-539, May-June.
    8. Cajas Guijarro, John, 2023. "Poder, intensidad del trabajo y crisis en un modelo marxista de ciclos endógenos," El Trimestre Económico, Fondo de Cultura Económica, vol. 90(358), pages 365-407, abril-jun.
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    10. Mehrling, Perry G, 1986. "A Classical Model of the Class Struggle: A Game-Theoretic Approach," Journal of Political Economy, University of Chicago Press, vol. 94(6), pages 1280-1303, December.
    11. Kleanthis Natsiopoulos & Nickolaos G. Tzeremes, 2022. "ARDL bounds test for cointegration: Replicating the Pesaran et al. (2001) results for the UK earnings equation using R," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 1079-1090, August.
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    More about this item

    Keywords

    Goodwin model; endogenous technical change; Hopf bifurcation; ARDL; numerical simulations;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E11 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Marxian; Sraffian; Kaleckian
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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