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Eventual periodicity in the two-sector RSL model: equilibrium vis-à-vis optimum growth

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But this long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task if in tempestuous seasons they can only tell us that when the storm is long past the ocean is flat again.

Keynes (1923)

Abstract

This paper investigates the well-known phenomenon of eventual periodicity of Li–Yorke chaos in the context of the two-sector Robinson–Shinkai–Leontief model of economic growth. It locates its (i) presence under specific parameter restrictions that include the extreme classical saving specification, and its (ii) absence in savings generated by the optimization of an infinitely-lived representative agent with perfect foresight. These results in which rare events, chaos and stability are all brought together under the rubric of upward and downward inertia, while of substantive economic interest of their own, also highlight phenomena in economic dynamics that may go towards a clearer definitional understanding of chaotic systems.

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Authors and Affiliations

  1. Division of Social Sciences, Yale-NUS College, Singapore, Singapore

    Liuchun Deng

  2. Department of Economics, Yokohama National University, Yokohama, Japan

    Minako Fujio

  3. Department of Economics, The Johns Hopkins University, Baltimore, MD, USA

    M. Ali Khan

Authors
  1. Liuchun Deng
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  2. Minako Fujio
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  3. M. Ali Khan
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Correspondence to Liuchun Deng.

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This paper is dedicated to the memory of T. N. Srinivasan, a pioneer of two-sector growth theory, a past editor of Econometrica, and also a mentor and role-model to so many others going well beyond the authors of this modest contribution, modest especially when keeping TN’s high standards in mind. Part of the results reported in this essay were presented at the 26th Annual Symposium of the Society for Nonlinear Dynamics and Econometrics in Keio University on March 19, 2018. The authors gratefully acknowledge stimulating conversation and exchanges with Bob Barbera, Jess Benhabib, Chris Carroll, Edmund Crawley, Tapan Mitra, Kazuo Nishimura, and Kevin Reffett, and finally, the encouragement of the Associate Editor of this journal and the careful reading of his/her two anonymous referees. Liuchun Deng acknowledges the support of the Start-up Grant from Yale-NUS College.

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Deng, L., Fujio, M. & Khan, M.A. Eventual periodicity in the two-sector RSL model: equilibrium vis-à-vis optimum growth. Econ Theory 72, 615–639 (2021). https://doi.org/10.1007/s00199-020-01301-0

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  • DOI: https://doi.org/10.1007/s00199-020-01301-0

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