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Exact parametric restrictions for 3-cycles in the RSS model: A complete and comprehensive characterization

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  • Deng, Liuchun
  • Khan, M. Ali
  • Mitra, Tapan

Abstract

This paper presents necessary and sufficient conditions for 3-period cycles in the two-sector Robinson–Solow–Srinivasan (RSS) model, taking as its point of departure an independently-(and simultaneously-) discovered exact discount-factor restriction for a general class of growth models by Mitra and Nishimura–Yano (MNY) in 1996. Our investigation of this remarkable result in the specificity of the RSS model enables a broadened inquiry that goes beyond the discount factor to parameters of labor-productivity and capital-depreciation. Since the RSS model, despite its concrete simplicity, is not covered by the general MNY model, the exact discount-factor restriction presented here does not follow from the MNY theorem, and necessitates new argumentation. Furthermore, we present a novel exact parametric region as our second result.

Suggested Citation

  • Deng, Liuchun & Khan, M. Ali & Mitra, Tapan, 2020. "Exact parametric restrictions for 3-cycles in the RSS model: A complete and comprehensive characterization," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 48-56.
    • Handle: RePEc:eee:mateco:v:90:y:2020:i:c:p:48-56
    DOI: 10.1016/j.jmateco.2020.05.008
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    References listed on IDEAS

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    1. Tapan Mitra & Gerhard Sorger, 1999. "Rationalizing Policy Functions by Dynamic Optimization," Econometrica, Econometric Society, vol. 67(2), pages 375-392, March.
    2. Kazuo Nishimura & Makoto Yano, 2012. "On the Least Upper Bound of Discount Factors that are Compatible with Optimal Period-Three Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 165-191, Springer.
    3. Khan, M. Ali & Mitra, Tapan, 2005. "On topological chaos in the Robinson-Solow-Srinivasan model," Economics Letters, Elsevier, vol. 88(1), pages 127-133, July.
    4. Deng Liuchun & Fujio Minako & Khan M. Ali, 2019. "Optimal growth in the Robinson-Shinkai-Leontief model: the case of capital-intensive consumption goods," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-18, September.
    5. Gerhard Sorger, 2018. "Cycles and chaos in the one-sector growth model with elastic labor supply," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(1), pages 55-77, January.
    6. M. Ali Khan & Tapan Mitra, 2005. "On choice of technique in the Robinson–Solow–Srinivasan model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(2), pages 83-110, June.
    7. Gerhard Sorger, 1994. "Period Three Implies Heavy Discounting," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 1007-1022, November.
    8. Mitra, Tapan, 1996. "An Exact Discount Factor Restriction for Period-Three Cycles in Dynamic Optimization Models," Journal of Economic Theory, Elsevier, vol. 69(2), pages 281-305, May.
    9. Deng Liuchun & Fujio Minako & Khan M. Ali, 2019. "Optimal growth in the Robinson-Shinkai-Leontief model: the case of capital-intensive consumption goods," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 23(4), pages 1-18, September.
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    Cited by:

    1. Ali Khan, M. & Zhang, Zhixiang, 2023. "The random two-sector RSS model: On discounted optimal growth without Ramsey-Euler conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    2. Augeraud-Veron, Emmanuelle & Boucekkine, Raouf & Gozzi, Fausto & Venditti, Alain & Zou, Benteng, 2024. "Fifty years of mathematical growth theory: Classical topics and new trends," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    3. Liuchun Deng & Minako Fujio & M. Ali Khan, 2022. "On Sustainability and Survivability in the Matchbox Two-Sector Model: A Complete Characterization of Optimal Extinction," Papers 2202.02209, arXiv.org.

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