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Some notes on discount factor restrictions for dynamic optimization problems

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  • Sorger, Gerhard

Abstract

We consider dynamic optimization problems on one-dimensional state spaces. Under standard smoothness and convexity assumptions, the optimal solutions are characterized by an optimal policy function h mapping the state space into itself. There exists an extensive literature on the relation between the size of the discount factor of the dynamic optimization problem on the one hand and the properties of the dynamical system xt+1=h(xt) on the other hand. The purpose of this paper is to survey some of the most important contributions of this literature and to modify or improve them in various directions. We deal in particular with the topological entropy of the dynamical system, with its Lyapunov exponents, and with its periodic orbits.

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  • Sorger, Gerhard, 2009. "Some notes on discount factor restrictions for dynamic optimization problems," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 435-448, July.
    • Handle: RePEc:eee:mateco:v:45:y:2009:i:7-8:p:435-448
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    References listed on IDEAS

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    1. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, vol. 59(5), pages 1365-1382, September.
    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. Gerhard Sorger, 2006. "Rationalizability in Optimal Growth Theory," Springer Books, in: Rose-Anne Dana & Cuong Le Van & Tapan Mitra & Kazuo Nishimura (ed.), Handbook on Optimal Growth 1, chapter 4, pages 85-113, Springer.
    4. Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521551861.
    5. 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.
    6. Tapan Mitra & Gerhard Sorger, 1999. "Rationalizing Policy Functions by Dynamic Optimization," Econometrica, Econometric Society, vol. 67(2), pages 375-392, March.
    7. Sorger, Gerhard, 1995. "On the sensitivity of optimal growth paths," Journal of Mathematical Economics, Elsevier, vol. 24(4), pages 353-369.
    8. Mitra, Tapan, 1998. "On the relationship between discounting and complicated behavior in dynamic optimization models," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 421-434, January.
    9. Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521558747.
    10. Montrucchio, Luigi & Sorger, Gerhard, 1996. "Topological entropy of policy functions in concave dynamic optimization models," Journal of Mathematical Economics, Elsevier, vol. 25(2), pages 181-194.
    11. Gerhard Sorger, 1994. "Period Three Implies Heavy Discounting," Mathematics of Operations Research, INFORMS, vol. 19(4), pages 1007-1022, November.
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    Cited by:

    1. Alain Venditti, 2012. "Weak concavity properties of indirect utility functions in multisector optimal growth models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 13-26, March.

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    More about this item

    Keywords

    Dynamic optimization Discounting Topological entropy Lyapunov exponents Periodic orbits;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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