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A simple model of growth cycles with technology choice

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  • Umezuki, Yosuke
  • Yokoo, Masanori

Abstract

In this study, we develop a simple, computable overlapping generations model that exhibits endogenous fluctuations. The key assumption is that a firm can choose from multiple technologies of production. Since the model reduces to a piecewise linear map on the unit interval, it allows us to conduct an in-depth analysis of its dynamic properties. Particularly, this piecewise linearization reveals the ability of the model to exhibit periodic attracting cycles of an arbitrarily large period as well as non-periodic attractors. Furthermore, it is demonstrated that the occurrence of periodic patterns is completely characterized by the rotation number or the “devil’s staircase.”

Suggested Citation

  • Umezuki, Yosuke & Yokoo, Masanori, 2019. "A simple model of growth cycles with technology choice," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 164-175.
    • Handle: RePEc:eee:dyncon:v:100:y:2019:i:c:p:164-175
    DOI: 10.1016/j.jedc.2018.11.006
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    References listed on IDEAS

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    1. Yokoo, Masanori & Ishida, Junichiro, 2008. "Misperception-driven chaos: Theory and policy implications," Journal of Economic Dynamics and Control, Elsevier, vol. 32(6), pages 1732-1753, June.
    2. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    3. Michel, Philippe & de la Croix, David, 2000. "Myopic and perfect foresight in the OLG model," Economics Letters, Elsevier, vol. 67(1), pages 53-60, April.
    4. Asano, Takao & Yokoo, Masanori, 2019. "Chaotic dynamics of a piecewise linear model of credit cycles," Journal of Mathematical Economics, Elsevier, vol. 80(C), pages 9-21.
    5. Kiminori Matsuyama, 2007. "Credit Traps and Credit Cycles," American Economic Review, American Economic Association, vol. 97(1), pages 503-516, March.
    6. Iwaisako, Tatsuro, 2002. "Technology choice and patterns of growth in an overlapping generations model," Journal of Macroeconomics, Elsevier, vol. 24(2), pages 211-231, June.
    7. Chen, Hung-Ju & Li, Ming-Chia & Lin, Yung-Ju, 2008. "Chaotic dynamics in an overlapping generations model with myopic and adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 48-56, July.
    8. Benhabib, Jess & Day, Richard H., 1982. "A characterization of erratic dynamics in, the overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 37-55, November.
    9. Ishida, Junichiro & Yokoo, Masanori, 2004. "Threshold nonlinearities and asymmetric endogenous business cycles," Journal of Economic Behavior & Organization, Elsevier, vol. 54(2), pages 175-189, June.
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    Citations

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    Cited by:

    1. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2024. "Technology choice, externalities in production, and a chaotic middle-income trap," Journal of Economics, Springer, vol. 141(1), pages 29-56, January.
    2. Gardini, Laura & Radi, Davide & Schmitt, Noemi & Sushko, Iryna & Westerhoff, Frank, 2023. "Sentiment-driven business cycle dynamics: An elementary macroeconomic model with animal spirits," Journal of Economic Behavior & Organization, Elsevier, vol. 210(C), pages 342-359.
    3. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2021. "Polarization and Permanent Fluctuations: Quasi-Periodic Motions in a Two-Class OLG Model (Revised version with a new title "Quasi-Periodic Motions in a Polarized Overlapping Generations Model wit," KIER Working Papers 1063, Kyoto University, Institute of Economic Research.
    4. Takao Asano & Akihisa Shibata & Masanori Yokoo, 2021. "Quasi-Periodic Motions in a Polarized Overlapping Generations Model with Technology Choice," KIER Working Papers 1070, Kyoto University, Institute of Economic Research.
    5. Jos'e Pedro Gaiv~ao & Benito Pires, 2022. "Chaotic time series in financial processes consisting of savings with piecewise constant monthly contributions," Papers 2206.11933, arXiv.org, revised Feb 2023.
    6. Liu, Taoxiong & Liu, Zhuohao, 2022. "A growth model with endogenous technological revolutions and cycles," Journal of Mathematical Economics, Elsevier, vol. 103(C).

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    More about this item

    Keywords

    Technology choice; Piecewise linearity; Endogenous fluctuations; Overlapping generations model; Rotation number; Devil’s staircase;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O14 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Industrialization; Manufacturing and Service Industries; Choice of Technology
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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