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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. 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.
    2. Chang,Fwu-Ranq, 2009. "Stochastic Optimization in Continuous Time," Cambridge Books, Cambridge University Press, number 9780521541947, September.
    3. 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.
    4. repec:cor:louvrp:-1755 is not listed on IDEAS
    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. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    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. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
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    Cited by:

    1. Simone Marsiglio & Davide La Torre, 2012. "A note on demographic shocks in a multi-sector growth model," Economics Bulletin, AccessEcon, vol. 32(3), pages 2293-2299.
    2. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    3. Liao, Zhong-Wei & Shao, Jinghai, 2024. "Stability and mean growth rate of stochastic Solow model driven by jump–diffusion process," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    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.
    5. Tsuboi, Mizuki, 2020. "Growth, R&D, and uncertainty," Economic Modelling, Elsevier, vol. 87(C), pages 394-400.

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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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