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Reviving Kalecki’s business cycle model in a growth context

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  • Franke, Reiner

Abstract

In 1935 Kalecki formulated the first fully specified model of a macroeconomic dynamics in which he studied an endogenous and most elementary business cycle mechanism. To revive his insights, the present paper adapts his stationary economy to a growth context. Introducing a reasonable nonlinearity into the investment function, it then takes care that the model exhibits persistent cyclical behaviour that is characterized by a unique, globally attracting limit cycle. This feature is a robust property. A calibration of the numerical parameters achieves desired values for the cycle period as well as the amplitudes of the output-capital ratio and the capital growth rate. It is moreover demonstrated that a one-time shock to the dynamics can easily have long-lasting effects on the amplitudes. Despite common misgivings about delay differential equations (which here result from Kalecki’s implementation lag), the analysis can be conducted with a limited mathematical effort.

Suggested Citation

  • Franke, Reiner, 2018. "Reviving Kalecki’s business cycle model in a growth context," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 157-171.
    • Handle: RePEc:eee:dyncon:v:91:y:2018:i:c:p:157-171
    DOI: 10.1016/j.jedc.2017.12.009
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    References listed on IDEAS

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    1. Michal Kalecki, 1937. "A Theory of the Business Cycle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 77-97.
    2. Reiner Franke, 2017. "A simple approach to overcome the problems arising from the Keynesian stability condition," European Journal of Economics and Economic Policies: Intervention, Edward Elgar Publishing, vol. 14(1), pages 48-69, April.
    3. Yoshida, Hiroyuki & Asada, Toichiro, 2007. "Dynamic analysis of policy lag in a Keynes-Goodwin model: Stability, instability, cycles and chaos," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 441-469, March.
    4. He, Xue-Zhong & Li, Kai & Wei, Junjie & Zheng, Min, 2009. "Market stability switches in a continuous-time financial market with heterogeneous beliefs," Economic Modelling, Elsevier, vol. 26(6), pages 1432-1442, November.
    5. Chiarella,Carl & Flaschel,Peter & Franke,Reiner, 2011. "Foundations for a Disequilibrium Theory of the Business Cycle," Cambridge Books, Cambridge University Press, number 9780521369923, September.
    6. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    7. Paul Zak, 1999. "Kaleckian Lags in General Equilibrium," Review of Political Economy, Taylor & Francis Journals, vol. 11(3), pages 321-330.
    8. Reiner Franke, 2017. "What output-capital ratio to adopt for macroeconomic calibrations?," International Review of Applied Economics, Taylor & Francis Journals, vol. 31(2), pages 208-224, March.
    9. Marek Szydłowski & Adam Krawiec, 2004. "A note on Kaleckian lags in the Solow model," Review of Political Economy, Taylor & Francis Journals, vol. 16(4), pages 501-506.
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    Citations

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    Cited by:

    1. Hartwig, Johannes, 2022. "Semi-endogenous growth dynamics in a macroeconomic model with delays," Structural Change and Economic Dynamics, Elsevier, vol. 62(C), pages 538-551.
    2. Tomas Ruzgas & Irma Jankauskienė & Audrius Zajančkauskas & Mantas Lukauskas & Matas Bazilevičius & Rugilė Kaluževičiūtė & Jurgita Arnastauskaitė, 2024. "Solving Linear and Nonlinear Delayed Differential Equations Using the Lambert W Function for Economic and Biological Problems," Mathematics, MDPI, vol. 12(17), pages 1-15, September.
    3. Barrales-Ruiz, Jose & Arnim, Rudiger von, 2021. "Endogenous fluctuations in demand and distribution: An empirical investigation," Structural Change and Economic Dynamics, Elsevier, vol. 58(C), pages 204-220.
    4. De Cesare, Luigi & Sportelli, Mario, 2022. "A non-linear approach to Kalecki’s investment cycle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 57-70.
    5. Sordi, Serena & Dávila-Fernández, Marwil J., 2022. "A two-stroke growth cycle model for a small open economy," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    6. Matsumoto, Akio & Szidarovszky, Ferenc, 2023. "Delay Solow Model with a Normalized CES Production Function," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 305-323.
    7. Marwil J. Dávila-Fernández & Serena Sordi, 2021. "Thirlwall's law: Binding-constraint or centre-of-gravity? A possible Kaleckian solution," Department of Economics University of Siena 853, Department of Economics, University of Siena.
    8. Robert A. Blecker, 2022. "New advances and controversies in the framework of balance‐of‐payments‐constrained growth," Journal of Economic Surveys, Wiley Blackwell, vol. 36(2), pages 429-467, April.
    9. Franke, Reiner, 2022. "An empirical test of a fundamental Harrod-Kaldor business cycle model," Structural Change and Economic Dynamics, Elsevier, vol. 60(C), pages 1-14.

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    More about this item

    Keywords

    Gestation period; Delay differential equations; Unique limit cycle; Calibration; Variations in the amplitude;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • E12 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Keynes; Keynesian; Post-Keynesian; Modern Monetary Theory
    • E30 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - General (includes Measurement and Data)

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