IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/200317.html
   My bibliography  Save this paper

Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth

Author

Listed:
  • Reiß, Markus
  • Bethmann, Dirk

Abstract

We introduce an easy way of analyzing the transitional dynamics of the Uzawa-Lucas endogenous growth model. We use the value function approach to solve both the social planner?s optimization problem and the representative agent?s optimization problem in the decentralized economy. The complexity of the Hamilton-Jacobi-Bellman equation is significantly reduced to a one-dimensional initial value problem for an ordinary differential equation. This approach allows us to find the optimal controls for the non-concave Hamiltonian in the centralized economy and to detect multiple transition paths in the decentralized economy for a large external effect, which are hidden when using the maximum principle. We simulate the global transitional dynamics towards the balanced growth path. The adjustment of the model?s state variable turns out to accelerate along the transition paths. By the asymmetry of the sectors an until now unknown feature is predicted for the adjustment in the output growth rate. Its relative speed follows a hump-shaped course: Starting from a relative scarcity in physical capital, the growth rate of output decelerates first before it starts rising again.

Suggested Citation

  • Reiß, Markus & Bethmann, Dirk, 2003. "Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth," SFB 373 Discussion Papers 2003,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200317
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/22232/1/dpsfb200317.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Robert J. Barro, 2013. "Inflation and Economic Growth," Annals of Economics and Finance, Society for AEF, vol. 14(1), pages 121-144, May.
    2. Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
    3. Bond, Eric W. & Wang, Ping & Yip, Chong K., 1996. "A General Two-Sector Model of Endogenous Growth with Human and Physical Capital: Balanced Growth and Transitional Dynamics," Journal of Economic Theory, Elsevier, vol. 68(1), pages 149-173, January.
    4. Xie Danyang, 1994. "Divergence in Economic Performance: Transitional Dynamics with Multiple Equilibria," Journal of Economic Theory, Elsevier, vol. 63(1), pages 97-112, June.
    5. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(3), pages 739-773.
    6. Caballe, Jordi & Santos, Manuel S, 1993. "On Endogenous Growth with Physical and Human Capital," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1042-1067, December.
    7. Rubio, Santiago J. & Casino, Begona, 2001. "Competitive versus efficient extraction of a common property resource: The groundwater case," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1117-1137, August.
    8. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May.
    9. Casey B. Mulligan & Xavier Sala-i-Martin, 1991. "A Note on the Time-Elimination Method For Solving Recursive Dynamic Economic Models," NBER Technical Working Papers 0116, National Bureau of Economic Research, Inc.
    10. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    11. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    12. P.M. Hartley & L.C.G. Rogers, 2005. "Two‐Sector Stochastic Growth Models," Australian Economic Papers, Wiley Blackwell, vol. 44(4), pages 322-351, December.
    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. Dirk Bethmann, 2005. "Notes on an Endogenous Growth Model with two Capital Stocks II: The Stochastic Case," SFB 649 Discussion Papers SFB649DP2005-033, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Dirk Bethmann, 2007. "A Closed-form Solution of the Uzawa-Lucas Model of Endogenous Growth," Journal of Economics, Springer, vol. 90(1), pages 87-107, January.

    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. Dirk Bethmann & Markus Reiß, 2012. "Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations," Journal of Economics, Springer, vol. 107(2), pages 101-128, October.
    2. Pedro Garcia-Castrillo & Marcos Sanso, 2000. "Human Capital and Optimal Policy in a Lucas-type Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(4), pages 757-770, October.
    3. 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.
    4. Garcia-Belenguer, Fernando, 2007. "Stability, global dynamics and Markov equilibrium in models of endogenous economic growth," Journal of Economic Theory, Elsevier, vol. 136(1), pages 392-416, September.
    5. Jaime Alonso-Carrera, 2001. "More on the dynamics in the endogenous growth model with human capital," Investigaciones Economicas, Fundación SEPI, vol. 25(3), pages 561-583, September.
    6. De, Supriyo, 2014. "Intangible capital and growth in the ‘new economy’: Implications of a multi-sector endogenous growth model," Structural Change and Economic Dynamics, Elsevier, vol. 28(C), pages 25-42.
    7. J. R. Ruiz-Tamarit & M. Ventura-Marco, "undated". "The Reduction of Dimension in the Study of Economic Growth Models," Working Papers 2001-13, FEDEA.
    8. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    9. Chilarescu, Constantin, 2011. "On the existence and uniqueness of solution to the Lucas–Uzawa model," Economic Modelling, Elsevier, vol. 28(1), pages 109-117.
    10. Bethmann, Dirk, 2008. "The open-loop solution of the Uzawa-Lucas model of endogenous growth with N agents," Journal of Macroeconomics, Elsevier, vol. 30(1), pages 396-414, March.
    11. 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.
    12. Olaf Posch & Timo Trimborn, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Economics Working Papers 2010-08, Department of Economics and Business Economics, Aarhus University.
    13. Benhabib, Jess & Gali, Jordi, 1995. "On growth and indeterminacy: some theory and evidence," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 43(1), pages 163-211, December.
    14. Kejak, Michal, 2003. "Stages of growth in economic development," Journal of Economic Dynamics and Control, Elsevier, vol. 27(5), pages 771-800, March.
    15. 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.
    16. Koch, Karl-Josef, 1995. "Stability issues of endogenous growth models," Discussion Papers, Series II 270, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    17. Klaus Wälde, 1996. "Proof of global stability, transitional dynamics, and international capital flows in a two-country model of innovation and growth," Journal of Economics, Springer, vol. 64(1), pages 53-84, February.
    18. Long, N.V. & Wong, K.Y., 1996. "Endogenous Growth and International Trade: A Survey," Working Papers 96-07, University of Washington, Department of Economics.
    19. Klaus Waelde, 1994. "Transitional dynamics, convergence and international capital flows in two-country models of innovation and growth," International Trade 9403002, University Library of Munich, Germany, revised 03 Jan 1996.
    20. Christian Ghiglino & Kazuo Nishimura & Alain Venditti, 2018. "Non-Balanced Endogenous Growth and Structural Change: When Romer Meets Kaldor and Kuznets," Working Papers halshs-01934872, HAL.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O4 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity

    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:zbw:sfb373:200317. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.html .

    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.