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Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology

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  • Darong Dai

    (School of Business, Nanjing University)

Abstract

In this paper, a stochastic endogenous aggregative growth model is constructed and two main results are established, based on endogenous horizon of the economy and endogenous terminal capital stock, which is also efficient capital accumulation in some sense. First, strong turnpike theorems under uncertainty and in the sense of uniform topology are obtained; second, inefficacy of temporary fiscal policy, which is chosen to be capital income taxation, has been demonstrated in comparatively weak conditions different from Yano (1998)'s.

Suggested Citation

  • Darong Dai, 2012. "Stochastic Versions of Turnpike Theorems in the Sense of Uniform Topology," Annals of Economics and Finance, Society for AEF, vol. 13(2), pages 381-423, November.
    • Handle: RePEc:cuf:journl:y:2012:v:13:i:2:n:6:dai
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    References listed on IDEAS

    as
    1. Yano, Makoto, 1984. "The turnpike of dynamic general equilibrium paths and its insensitivity to initial conditions," Journal of Mathematical Economics, Elsevier, vol. 13(3), pages 235-254, December.
    2. Liutang Gong & Heng-fu Zou, 2003. "Fiscal Federalism, Public Capital Formation, and Endogenous Growth," Annals of Economics and Finance, Society for AEF, vol. 4(2), pages 471-490, November.
    3. Lionel W. McKenzie, 2012. "turnpike theory," The New Palgrave Dictionary of Economics,, Palgrave Macmillan.
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    7. Yano, Makoto, 1985. "Competitive Equilibria on Turnpikes in a McKenzie Economy, II: An Asymptotic Turnpike Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 661-669, October.
    8. Yano, Makoto, 1984. "Competitive Equilibria on Turnpikes in a McKenzie Economy, I: A Neighborhood Turnpike Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(3), pages 695-717, October.
    9. Turnovsky, Stephen J., 2000. "Fiscal policy, elastic labor supply, and endogenous growth," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 185-210, February.
    10. Liutang Gong & Heng-fu Zou, 2000. "Foreign Aid Reduces Domestic Capital Accumulation and Increases Foreign Borrowing: A Theoretical Analysis," Annals of Economics and Finance, Society for AEF, vol. 1(1), pages 147-163, May.
    11. Coles, Jeffrey Link, 1985. "Equilibrium Turnpike Theory with Constant Returns to Scale and Possible Heterogeneous Discount Factors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 671-679, October.
    12. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
    13. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
    14. M. Morishima, 1961. "Prices and the Turnpike: II. Proof of a Turnpike Theorem: The "No Joint Production" Case," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 89-97.
    15. Joshi, Sumit, 1997. "Turnpike Theorems in Nonconvex Nonstationary Environments," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(1), pages 225-248, February.
    16. Philippe Aghion, 2004. "Growth and Development: A Schumpeterian Approach," Annals of Economics and Finance, Society for AEF, vol. 5(1), pages 1-25, May.
    17. Roy Radner, 1961. "Prices and the Turnpike: III. Paths of Economic Growth that are Optimal with Regard only to Final States: A Turnpike Theorem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 28(2), pages 98-104.
    18. Makoto Yano, 1998. "On the Dual Stability of a von Neumann Facet and the Inefficacy of Temporary Fiscal Policy," Econometrica, Econometric Society, vol. 66(2), pages 427-452, March.
    19. Barro, Robert J, 1990. "Government Spending in a Simple Model of Endogenous Growth," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages 103-126, October.
    20. McKenzie, Lionel W., 1982. "A primal route to the Turnpike and Liapounov stability," Journal of Economic Theory, Elsevier, vol. 27(1), pages 194-209, June.
    21. Araujo, A & Scheinkman, Jose A, 1977. "Smoothness, Comparative Dynamics, and the Turnpike Property," Econometrica, Econometric Society, vol. 45(3), pages 601-620, April.
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    Citations

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    Cited by:

    1. Darong Dai, 2014. "A Golden Formula in Neoclassical-Growth Models with Brownian-Motion Shocks," Scottish Journal of Political Economy, Scottish Economic Society, vol. 61(2), pages 211-228, May.
    2. Dai, Darong, 2011. "Modeling the minimum time needed to economic maturity," MPRA Paper 40583, University Library of Munich, Germany, revised 08 Aug 2012.
    3. Dai, Darong, 2011. "Wealth Martingale and Neighborhood Turnpike Property in Dynamically Complete Market with Heterogeneous Investors," MPRA Paper 46416, University Library of Munich, Germany.
    4. Darong Dai, 2014. "On the Turnpike Property of the Modified Golden Rule," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 8(1), pages 26-32, August.
    5. Dai, Darong & Tian, Guoqiang, 2021. "Toward longer investment: Is an inclusive regime always better than an authoritarian one?," Economic Modelling, Elsevier, vol. 98(C), pages 41-68.
    6. Dai, Darong, 2012. "A Robust Turnpike Deduced by Economic Maturity," MPRA Paper 48818, University Library of Munich, Germany.
    7. Dai, Darong, 2013. "Cooperative economic growth," Economic Modelling, Elsevier, vol. 33(C), pages 407-415.
    8. Dai, Darong, 2012. "On the existence and stability of Pareto optimal endogenous matching with fairness," MPRA Paper 40457, University Library of Munich, Germany.
    9. Dai, Darong, 2012. "On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness," MPRA Paper 40560, University Library of Munich, Germany.
    10. Darong Dai, 2018. "Fiscal policy under a minimum‐time objective," Scottish Journal of Political Economy, Scottish Economic Society, vol. 65(3), pages 293-314, July.
    11. Darong Dai, 2015. "Robust Turnpikes Deduced by the Minimum-Time Needed toward Economic Maturity," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(1), pages 049-073, October.
    12. Dai, Darong, 2012. "Comparative Studies on Cooperative Stochastic Differential Game and Dynamic Sequential Game of Economic Maturity," MPRA Paper 44339, University Library of Munich, Germany.
    13. Darong Dai, 2014. "The Long-Run Behavior of Consumption and Wealth Dynamics in Complete Financial Market with Heterogeneous Investors," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-16, July.
    14. Darong Dai, 2013. "Wealth Martingale and Neighborhood Turnpike Property In Dynamically Complete Market With Heterogeneous Investors," Economic Research Guardian, Weissberg Publishing, vol. 3(2), pages 86-110, December.

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    More about this item

    Keywords

    Stochastic endogenous growth; Uniform-topology turnpike theorems; Endogenous terminal stock; Endogenous welfare function; Capital income taxation;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory

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