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The random two-sector RSS model: On discounted optimal growth without Ramsey-Euler conditions

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  • Ali Khan, M.
  • Zhang, Zhixiang

Abstract

This paper shows that the introduction of uncertainty in the two-sector model due to Robinson-Solow-Srinivasan (RSS) fully subdues the veritable plethora of the results that have been obtained the theory of deterministic optimal growth. Rather than an “anything goes” theorem that admits optimal cyclical and chaotic trajectories for the discrete-time deterministic version, we present results on the existence, uniqueness, asymptotic stability and comparative-static properties of the steady state measure. We relate the basic intuition of our result to global games, and note that the properties of value and policy functions we identify rely on “supermodularity” and “increasing-differences property” of Veinott-Topkis-Milgrom-Shannon. While of interest in themselves, our results highlight a methodological advance in developing the theory of optimal growth without Ramsey-Euler conditions.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:dyncon:v:146:y:2023:i:c:s016518892200286x
    DOI: 10.1016/j.jedc.2022.104583
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    1. , & ,, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    2. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    3. Jean-Charles Rochet & Xavier Vives, 2004. "Coordination Failures and the Lender of Last Resort: Was Bagehot Right After All?," Journal of the European Economic Association, MIT Press, vol. 2(6), pages 1116-1147, December.
    4. Morris, Stephen & Shin, Hyun Song, 1998. "Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks," American Economic Review, American Economic Association, vol. 88(3), pages 587-597, June.
    5. Khan, M. Ali & Mitra, Tapan, 2012. "Long-Run Optimal Behavior In A Two-Sector Robinson–Solow–Srinivasan Model," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S1), pages 70-85, April.
    6. Kamihigashi, Takashi & Roy, Santanu, 2007. "A nonsmooth, nonconvex model of optimal growth," Journal of Economic Theory, Elsevier, vol. 132(1), pages 435-460, January.
    7. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    8. Zhang, Yuzhe, 2007. "Stochastic optimal growth with a non-compact state space," Journal of Mathematical Economics, Elsevier, vol. 43(2), pages 115-129, February.
    9. Chatterjee, Partha & Shukayev, Malik, 2008. "Note on positive lower bound of capital in the stochastic growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2137-2147, July.
    10. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    11. Stigum, Bernt P., 1972. "Balanced growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 5(1), pages 42-68, August.
    12. George-Marios Angeletos & Christian Hellwig & Alessandro Pavan, 2007. "Dynamic Global Games of Regime Change: Learning, Multiplicity, and the Timing of Attacks," Econometrica, Econometric Society, vol. 75(3), pages 711-756, May.
    13. Stephen Morris & Hyun Song Shin, 2001. "Rethinking Multiple Equilibria in Macroeconomic Modeling," NBER Chapters, in: NBER Macroeconomics Annual 2000, Volume 15, pages 139-182, National Bureau of Economic Research, Inc.
    14. Takashi Kamihigashi & Santanu Roy, 2006. "Dynamic optimization with a nonsmooth, nonconvex technology: the case of a linear objective function," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(2), pages 325-340, October.
    15. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    16. Robert C. Merton, 1975. "An Asymptotic Theory of Growth Under Uncertainty," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 375-393.
    17. Stachurski, John, 2002. "Stochastic Optimal Growth with Unbounded Shock," Journal of Economic Theory, Elsevier, vol. 106(1), pages 40-65, September.
    18. Sun, Xiang & Sun, Yeneng & Yu, Haomiao, 2020. "The individualistic foundation of equilibrium distribution," Journal of Economic Theory, Elsevier, vol. 189(C).
    19. Stachurski, John, 2003. "Economic dynamical systems with multiplicative noise," Journal of Mathematical Economics, Elsevier, vol. 39(1-2), pages 135-152, February.
    20. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 477-500, April.
    21. Ali Khan, M. & Mitra, Tapan, 2008. "Growth in the Robinson-Solow-Srinivasan model: Undiscounted optimal policy with a strictly concave welfare function," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 707-732, July.
    22. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
    23. Kazuo Nishimura & John Stachurski, 2012. "Stability of Stochastic Optimal Growth Models: A New Approach," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 289-307, Springer.
    24. 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.
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    More about this item

    Keywords

    Stochastic optimal growth; Discounting; 2-Sector RSS model; Ramsey-Euler conditions;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O21 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Planning Models; Planning Policy

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