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On a closed-form solution to the stochastic Lucas–Uzawa model

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  • Ryoji Hiraguchi

Abstract

Bucci et al. (J Econ 103:83–99, 2011 ) argue that under two parametric restrictions, there exists a closed-form solution path to the two-sector endogenous growth model of Lucas–Uzawa. However, they assume that the value function is a function of both the current and the initial values of the state variables. As Wälde (J Econ Dyn Control 35:616–622, 2011a ) argues, the value function should depend only on the current state variables when the technology follows a geometric Brownian motion. I follow Wälde (J Econ Dyn Control 35:616–622, 2011a ) and obtain, under some inequality constraints, a different value function. Copyright Springer-Verlag 2013

Suggested Citation

  • Ryoji Hiraguchi, 2013. "On a closed-form solution to the stochastic Lucas–Uzawa model," Journal of Economics, Springer, vol. 108(2), pages 131-144, March.
    • Handle: RePEc:kap:jeczfn:v:108:y:2013:i:2:p:131-144
    DOI: 10.1007/s00712-012-0295-3
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    References listed on IDEAS

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    1. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, November.
    2. Boucekkine Raouf & Ruiz Tamarit Ramon, 2004. "Imbalance Effects in the Lucas Model: an Analytical Exploration," The B.E. Journal of Macroeconomics, De Gruyter, vol. 4(1), pages 1-19, December.
    3. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    4. Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
    5. A. Bucci & C. Colapinto & M. Forster & D. La Torre, 2011. "Stochastic technology shocks in an extended Uzawa–Lucas model: closed-form solution and long-run dynamics," Journal of Economics, Springer, vol. 103(1), pages 83-99, May.
    6. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    7. Smith William T, 2007. "Inspecting the Mechanism Exactly: A Closed-form Solution to a Stochastic Growth Model," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-33, August.
    8. repec:cor:louvrp:-1755 is not listed on IDEAS
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    Cited by:

    1. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
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    4. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.

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    More about this item

    Keywords

    Endogenous growth; Closed-form solution; Value function; Brownian motion; E5;
    All these keywords.

    JEL classification:

    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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