IDEAS home Printed from https://ideas.repec.org/a/kap/jeczfn/v108y2013i2p131-144.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00712-012-0295-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00712-012-0295-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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. 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.
    5. 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.
    6. repec:cor:louvrp:-1755 is not listed on IDEAS
    7. 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.
    8. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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).
    2. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    3. Tsuboi, Mizuki, 2020. "Growth, R&D, and uncertainty," Economic Modelling, Elsevier, vol. 87(C), pages 394-400.
    4. 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.
    5. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tsuboi, Mizuki, 2019. "Resource scarcity, technological progress, and stochastic growth," Economic Modelling, Elsevier, vol. 81(C), pages 73-88.
    2. Robert Feicht & Wolfgang Stummer, 2010. "Complete Closed-form Solution to a Stochastic Growth Model and Corresponding Speed of Economic Recovery preliminary," DEGIT Conference Papers c015_041, DEGIT, Dynamics, Economic Growth, and International Trade.
    3. Tsuboi, Mizuki, 2019. "Consumption, welfare, and stochastic population dynamics when technology shocks are (Un)tied," Economic Modelling, Elsevier, vol. 79(C), pages 74-85.
    4. Mizuki Tsuboi, 2018. "Stochastic accumulation of human capital and welfare in the Uzawa–Lucas model: an analytical characterization," Journal of Economics, Springer, vol. 125(3), pages 239-261, November.
    5. Alberto Bucci & Simone Marsiglio, 2019. "Financial development and economic growth: long‐run equilibrium and transitional dynamics," Scottish Journal of Political Economy, Scottish Economic Society, vol. 66(3), pages 331-359, July.
    6. Constantin Chilarescu, 2018. "The effect of externality on the transitional dynamics: the case of Lucas model," Economics Bulletin, AccessEcon, vol. 32767(3).
    7. Raouf Boucekkine & Bity Diene & Theophile Azomahou, 2008. "Growth Economics of Epidemics: A Review of the Theory," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(1), pages 1-26.
    8. Bosi, Stefano & Camacho, Carmen & Ha-Huy, Thai, 2023. "Balanced growth and degrowth with human capital," Economics Letters, Elsevier, vol. 232(C).
    9. 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.
    10. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    11. Posch, Olaf, 2011. "Explaining output volatility: The case of taxation," Journal of Public Economics, Elsevier, vol. 95(11), pages 1589-1606.
    12. Hiraguchi, Ryoji, 2009. "A solution to the Lucas-Uzawa model with increasing returns to scale: Note," Economic Modelling, Elsevier, vol. 26(5), pages 831-834, September.
    13. Chilarescu, Constantin, 2011. "On the existence and uniqueness of solution to the Lucas–Uzawa model," Economic Modelling, Elsevier, vol. 28(1), pages 109-117.
    14. Ruiz-Tamarit, José Ramón, 2008. "The closed-form solution for a family of four-dimension nonlinear MHDS," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 1000-1014, March.
    15. Tsuboi, Mizuki, 2020. "Growth, R&D, and uncertainty," Economic Modelling, Elsevier, vol. 87(C), pages 394-400.
    16. José Ramón Ruiz Tamarit & Manuel Sánchez Moreno, 2006. "Optimal Regulation And Growth In A Natural-Resource-Based Economy," Working Papers. Serie AD 2006-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    17. Brito, Paulo & Venditti, Alain, 2010. "Local and global indeterminacy in two-sector models of endogenous growth," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 893-911, September.
    18. Dirk Bethmann & Markus Reiß, 2012. "Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations," Journal of Economics, Springer, vol. 107(2), pages 101-128, October.
    19. Chilarescu, Constantin, 2009. "A closed-form solution to the transitional dynamics of the Lucas-Uzawa model," Economic Modelling, Elsevier, vol. 26(1), pages 135-138, January.
    20. Marsiglio, Simone & La Torre, Davide, 2012. "Population dynamics and utilitarian criteria in the Lucas–Uzawa Model," Economic Modelling, Elsevier, vol. 29(4), pages 1197-1204.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jeczfn:v:108:y:2013:i:2:p:131-144. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.